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]);
    }

}
/tmp/hf-datasets-cache/medium/datasets/42704881117311-config-parquet-and-info-qiankunmu-Project_CodeNet-896c9d36/hub/datasets--qiankunmu--Project_CodeNet_Python800_and_Java250/snapshots/c899fde44a77ba1cc14973ed3de064e4ff3aadc7/Project_CodeNet_Java250.tar.gz