import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int k = scanner.nextInt();
        int n = scanner.nextInt();

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

        int maxDistance = 0;
        for (int i = 1; i < n; i++) {
            maxDistance = Math.max(maxDistance, a[i]-a[i-1]);
        }
        maxDistance = Math.max(maxDistance, a[0]+k-a[n-1]);

        System.out.println(k-maxDistance);


    }
}

/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