import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author L_aka_ryuga
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}
 import java.io.OutputStream; OutputStream java.io import java.io.IOException; IOException java.io import java.io.InputStream; InputStream java.io import java.io.OutputStream; OutputStream java.io import java.io.PrintWriter; PrintWriter java.io import java.io.BufferedWriter; BufferedWriter java.io import java.io.Writer; Writer java.io import java.io.OutputStreamWriter; OutputStreamWriter java.io import java.util.InputMismatchException; InputMismatchException java.util import java.io.IOException; IOException java.io import java.io.InputStream; InputStream java.io public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
} Main public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    } main {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    } InputStream inputStream = System.in; inputStream System.in System System.in OutputStream outputStream = System.out; outputStream System.out System System.out InputReader in = new InputReader(inputStream); in new InputReader(inputStream) OutputWriter out = new OutputWriter(outputStream); out new OutputWriter(outputStream) CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake(); solver new CTravelingSalesmanAroundLake() solver.solve(1, in, out) solver.solve solver 1 in out out.close() out.close out String[] args args static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    } CTravelingSalesmanAroundLake public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        } solve {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        } int k = in.ni() k in.ni() in.ni in n = in.ni(); n in.ni() in.ni in int[] arr = in.nia(n); arr in.nia(n) in.nia in n long sum = 0; sum 0 for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]); int i = 0; int i = 0; i 0 i < n - 1 i n - 1 n 1 i++ i++ i sum += (arr[i + 1] - arr[i]); sum += (arr[i + 1] - arr[i]) sum (arr[i + 1] - arr[i]) arr[i + 1] arr i + 1 i 1 arr[i] arr i long min = sum; min sum long valtoadd = (k - arr[n - 1]) + arr[0]; valtoadd (k - arr[n - 1]) + arr[0] (k - arr[n - 1]) k arr[n - 1] arr n - 1 n 1 arr[0] arr 0 for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            } int i = 1; int i = 1; i 1 i < n i n i++ i++ i {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            } {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            } long ans = sum + valtoadd - (arr[i] - arr[i - 1]); ans sum + valtoadd - (arr[i] - arr[i - 1]) sum + valtoadd sum valtoadd (arr[i] - arr[i - 1]) arr[i] arr i arr[i - 1] arr i - 1 i 1 min = Math.min(min, ans) min Math.min(min, ans) Math.min Math min ans out.println(min) out.println out min int testNumber testNumber InputReader in in OutputWriter out out static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    } InputReader private InputStream stream; stream private byte[] buf = new byte[1024]; buf new byte[1024] 1024 private int curChar; curChar private int numChars; numChars private InputReader.SpaceCharFilter filter; filter public InputReader(InputStream stream) {
            this.stream = stream;
        } InputReader {
            this.stream = stream;
        } this.stream = stream this.stream this this.stream stream InputStream stream stream public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        } read {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        } if (numChars == -1) {
                throw new InputMismatchException();
            } numChars == -1 numChars -1 1 {
                throw new InputMismatchException();
            } throw new InputMismatchException(); new InputMismatchException() if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            } curChar >= numChars curChar numChars {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            } curChar = 0 curChar 0 try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                } catch (IOException e) {
                    throw new InputMismatchException();
                } IOException e {
                    throw new InputMismatchException();
                } throw new InputMismatchException(); new InputMismatchException() {
                    numChars = stream.read(buf);
                } numChars = stream.read(buf) numChars stream.read(buf) stream.read stream buf if (numChars <= 0) {
                    return -1;
                } numChars <= 0 numChars 0 {
                    return -1;
                } return -1; -1 1 return buf[curChar++]; buf[curChar++] buf curChar++ curChar public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } ni {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } int c = read(); c read() read while (isSpaceChar(c)) {
                c = read();
            } isSpaceChar(c) isSpaceChar c {
                c = read();
            } c = read() c read() read int sgn = 1; sgn 1 if (c == '-') {
                sgn = -1;
                c = read();
            } c == '-' c '-' {
                sgn = -1;
                c = read();
            } sgn = -1 sgn -1 1 c = read() c read() read int res = 0; res 0 do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c)); !isSpaceChar(c) isSpaceChar(c) isSpaceChar c {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                } c < '0' || c > '9' c < '0' c '0' c > '9' c '9' {
                    throw new InputMismatchException();
                } throw new InputMismatchException(); new InputMismatchException() res *= 10 res 10 res += c - '0' res c - '0' c '0' c = read() c read() read return res * sgn; res * sgn res sgn public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        } isSpaceChar {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        } if (filter != null) {
                return filter.isSpaceChar(c);
            } filter != null filter null {
                return filter.isSpaceChar(c);
            } return filter.isSpaceChar(c); filter.isSpaceChar(c) filter.isSpaceChar filter c return isWhitespace(c); isWhitespace(c) isWhitespace c int c c public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        } isWhitespace {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        } return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1 c == '\t' c == '\r' c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1 c == ' ' c ' ' c == '\n' c '\n' c == '\r' c '\r' c == '\t' c '\t' c == -1 c -1 1 int c c public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        } nia {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        } int[] array = new int[n]; array new int[n] n for (int i = 0; i < n; ++i) array[i] = ni(); int i = 0; int i = 0; i 0 i < n i n ++i ++i i array[i] = ni(); array[i] = ni() array[i] array i ni() ni return array; array int n n public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        } SpaceCharFilter public boolean isSpaceChar(int ch); isSpaceChar int ch ch static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    } OutputWriter private final PrintWriter writer; writer public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        } OutputWriter {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        } writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))) writer new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))) OutputStream outputStream outputStream public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        } OutputWriter {
            this.writer = new PrintWriter(writer);
        } this.writer = new PrintWriter(writer) this.writer this this.writer new PrintWriter(writer) Writer writer writer public void close() {
            writer.close();
        } close {
            writer.close();
        } writer.close() writer.close writer public void println(long i) {
            writer.println(i);
        } println {
            writer.println(i);
        } writer.println(i) writer.println writer i long i i public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
} public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
} Main
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author L_aka_ryuga
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int k = in.ni(), n = in.ni();
            int[] arr = in.nia(n);


            long sum = 0;
            for (int i = 0; i < n - 1; i++) sum += (arr[i + 1] - arr[i]);

            long min = sum;
            long valtoadd = (k - arr[n - 1]) + arr[0];
            for (int i = 1; i < n; i++) {
                long ans = sum + valtoadd - (arr[i] - arr[i - 1]);
                min = Math.min(min, ans);
            }

            out.println(min);

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int[] nia(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = ni();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}

