import java.util.Scanner;

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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        System.out.println(k - max);
    }
} import java.util.Scanner; Scanner 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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        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 = 0; max 0 for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        } int i=0; int i=0; i 0 i<n i n i++ i++ i {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        } {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        } int b; b if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            } i == n-1 i n-1 n 1 {
                b = a[0] + k - a[i];
            } b = a[0] + k - a[i] b a[0] + k - a[i] a[0] + k a[0] a 0 k a[i] a i {
                b = a[i+1] - a[i];
            } b = a[i+1] - a[i] b a[i+1] - a[i] a[i+1] a i+1 i 1 a[i] a i if(b > max) max = b; b > max b max max = b max b 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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        System.out.println(k - max);
    }
} Main
import java.util.Scanner;

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 = 0;
        for(int i=0; i<n; i++) {
            int b;
            if(i == n-1) {
                b = a[0] + k - a[i];
            } else {
                b = a[i+1] - a[i];
            }
            if(b > max) max = b;
        }
        System.out.println(k - max);
    }
}
