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];
        int max_dist = 0;
        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }
        sc.close();
        max_dist = a[0] + (k - a[n - 1]);
        for(int i = 0; i < n - 1; i++){
            max_dist = Math.max(max_dist, a[i + 1] - a[i]);
        }
        System.out.println(k - max_dist);
    }
}
/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