import 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 = k - a[n - 1] + a[0];

        for(int i = 0; i < n - 1; i++){
            int sub = a[i + 1] - a[i];

            if(max < sub){
                max = sub;
            }
        }

        System.out.println(k - max);
    }
}

/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