import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    }

} import java.util.Arrays; Arrays java.util import java.util.Scanner; Scanner java.util public class Main {

    public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    }

} Main public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    } main {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    } @SuppressWarnings("resource")
        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[] b = new int[n]; b new int[n] n for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        } int i = 0 ; int i = 0 ; i 0 i < n - 1 i n - 1 n 1 i++ i++ i {
            b[i] = a[i + 1] - a[i];
        } {
            b[i] = a[i + 1] - a[i];
        } b[i] = a[i + 1] - a[i] b[i] b i a[i + 1] - a[i] a[i + 1] a i + 1 i 1 a[i] a i b[n - 1] = k - a[n - 1] + a[0] b[n - 1] b n - 1 n 1 k - a[n - 1] + a[0] k - a[n - 1] k a[n - 1] a n - 1 n 1 a[0] a 0 Arrays.sort(b) Arrays.sort Arrays b System.out.println(k - b[n - 1]) System.out.println System.out System System.out k - b[n - 1] k b[n - 1] b n - 1 n 1 String[] args args public class Main {

    public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    }

} public class Main {

    public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    }

} Main
import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        @SuppressWarnings("resource")
        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[] b = new int[n];
        for (int i = 0 ; i < n - 1 ; i++) {
            b[i] = a[i + 1] - a[i];
        }
        b[n - 1] = k - a[n - 1] + a[0];
        Arrays.sort(b);
        System.out.println(k - b[n - 1]);
    }

}