import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    }
} import java.io.BufferedReader; BufferedReader java.io import java.io.IOException; IOException java.io import java.io.InputStreamReader; InputStreamReader java.io import java.util.StringTokenizer; StringTokenizer java.util public class Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    }
} Main public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    } main {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    } FastReader obj = new FastReader(); obj new FastReader() int dist = obj.nextInt() dist obj.nextInt() obj.nextInt obj house = obj.nextInt() house obj.nextInt() obj.nextInt obj no_house[] = new int[house]; no_house new int[house] house for(int i=0;i<house;i++) no_house[i] = obj.nextInt(); int i=0; int i=0; i 0 i<house i house i++ i++ i no_house[i] = obj.nextInt(); no_house[i] = obj.nextInt() no_house[i] no_house i obj.nextInt() obj.nextInt obj int find[] = new int[house]; find new int[house] house for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        } int i=0; int i=0; i 0 i<house i house i++ i++ i {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        } {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        } if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1]; i==0 i 0 find[i] = no_house[no_house.length-1]-no_house[i] find[i] find i no_house[no_house.length-1]-no_house[i] no_house[no_house.length-1] no_house no_house.length-1 no_house.length no_house no_house.length 1 no_house[i] no_house i find[i] = (dist-no_house[i])+no_house[i-1] find[i] find i (dist-no_house[i])+no_house[i-1] (dist-no_house[i]) dist no_house[i] no_house i no_house[i-1] no_house i-1 i 1 int min = Integer.MAX_VALUE; min Integer.MAX_VALUE Integer Integer.MAX_VALUE for(int i=0;i<house;i++) min = Math.min(find[i],min); int i=0; int i=0; i 0 i<house i house i++ i++ i min = Math.min(find[i],min); min = Math.min(find[i],min) min Math.min(find[i],min) Math.min Math find[i] find i min System.out.println(min) System.out.println System.out System System.out min String args[] args static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    } FastReader BufferedReader br; br StringTokenizer st; st public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        } FastReader {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        } br = new BufferedReader(new
                    InputStreamReader(System.in)) br new BufferedReader(new
                    InputStreamReader(System.in)) String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        } next {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        } while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            } st == null || !st.hasMoreElements() st == null st null !st.hasMoreElements() st.hasMoreElements() st.hasMoreElements st {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            } try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (IOException e) {
                    e.printStackTrace();
                } IOException e {
                    e.printStackTrace();
                } e.printStackTrace() e.printStackTrace e {
                    st = new StringTokenizer(br.readLine());
                } st = new StringTokenizer(br.readLine()) st new StringTokenizer(br.readLine()) return st.nextToken(); st.nextToken() st.nextToken st int nextInt() {
            return Integer.parseInt(next());
        } nextInt {
            return Integer.parseInt(next());
        } return Integer.parseInt(next()); Integer.parseInt(next()) Integer.parseInt Integer next() next long nextLong() {
            return Long.parseLong(next());
        } nextLong {
            return Long.parseLong(next());
        } return Long.parseLong(next()); Long.parseLong(next()) Long.parseLong Long next() next double nextDouble() {
            return Double.parseDouble(next());
        } nextDouble {
            return Double.parseDouble(next());
        } return Double.parseDouble(next()); Double.parseDouble(next()) Double.parseDouble Double next() next String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        } nextLine {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        } String str = ""; str "" try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            } catch (IOException e) {
                e.printStackTrace();
            } IOException e {
                e.printStackTrace();
            } e.printStackTrace() e.printStackTrace e {
                str = br.readLine();
            } str = br.readLine() str br.readLine() br.readLine br return str; str public class Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    }
} public class Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    }
} Main
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String args[])
    {
        FastReader obj = new FastReader();
        int dist = obj.nextInt(),house = obj.nextInt(),no_house[] = new int[house];
        for(int i=0;i<house;i++) no_house[i] = obj.nextInt();
        int find[] = new int[house];
        for(int i=0;i<house;i++)
        {
            if(i==0)
                find[i] = no_house[no_house.length-1]-no_house[i];
            else
                find[i] = (dist-no_house[i])+no_house[i-1];
        }
        int min = Integer.MAX_VALUE;
        for(int i=0;i<house;i++) min = Math.min(find[i],min);
        System.out.println(min);
    }
}
