import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
} import java.util.*; util.* java public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
} Main public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    } main {
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    } Scanner sc = new Scanner(System.in); sc new Scanner(System.in) int k = sc.nextInt(); k sc.nextInt() sc.nextInt sc int n = sc.nextInt(); n sc.nextInt() sc.nextInt sc int[] a = new int [n]; a new int [n] n for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        } int i = 0; int i = 0; i 0 i < n i n i++ i++ i {
            a[i] = sc.nextInt();
        } {
            a[i] = sc.nextInt();
        } a[i] = sc.nextInt() a[i] a i sc.nextInt() sc.nextInt sc int max = k - a[n - 1] + a[0]; max k - a[n - 1] + a[0] k - a[n - 1] k a[n - 1] a n - 1 n 1 a[0] a 0 for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        } int i = 0; int i = 0; i 0 i < n - 1 i n - 1 n 1 i++ i++ i {
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        } {
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        } int sub = a[i + 1] - a[i]; sub a[i + 1] - a[i] a[i + 1] a i + 1 i 1 a[i] a i if(max < sub){
                max = sub;
            } max < sub max sub {
                max = sub;
            } max = sub max sub System.out.println(k - max) System.out.println System.out System System.out k - max k max String[] args args public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
} public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
} Main
import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int k = sc.nextInt();
        int n = sc.nextInt();

        int[] a = new int [n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        int max = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
}
