import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ky112233
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

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

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

    }
} Main public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    } main {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(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 Scanner in = new Scanner(inputStream); in new Scanner(inputStream) PrintWriter out = new PrintWriter(outputStream); out new PrintWriter(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, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

    } CTravelingSalesmanAroundLake public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        } solve {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        } int k = in.nextInt(); k in.nextInt() in.nextInt in int n = in.nextInt(); n in.nextInt() in.nextInt in int[] a = new int[n]; a new int[n] n for (int i = 0; i < n; i++) a[i] = in.nextInt(); int i = 0; int i = 0; i 0 i < n i n i++ i++ i a[i] = in.nextInt(); a[i] = in.nextInt() a[i] a i in.nextInt() in.nextInt in int mx = Math.abs(a[0] + k - a[n - 1]); mx Math.abs(a[0] + k - a[n - 1]) Math.abs Math a[0] + k - a[n - 1] a[0] + k a[0] a 0 k a[n - 1] a n - 1 n 1 for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            } int i = 1; int i = 1; i 1 i < n i n i++ i++ i {
                mx = Math.max(mx, a[i] - a[i - 1]);
            } {
                mx = Math.max(mx, a[i] - a[i - 1]);
            } mx = Math.max(mx, a[i] - a[i - 1]) mx Math.max(mx, a[i] - a[i - 1]) Math.max Math mx a[i] - a[i - 1] a[i] a i a[i - 1] a i - 1 i 1 out.println(k - mx) out.println out k - mx k mx int testNumber testNumber Scanner in in PrintWriter out out public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

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

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

    }
} Main
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ky112233
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CTravelingSalesmanAroundLake solver = new CTravelingSalesmanAroundLake();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTravelingSalesmanAroundLake {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int k = in.nextInt();
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = in.nextInt();
            int mx = Math.abs(a[0] + k - a[n - 1]);
            for (int i = 1; i < n; i++) {
                mx = Math.max(mx, a[i] - a[i - 1]);
            }
            out.println(k - mx);
        }

    }
}

