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();
        ArrayList<Integer> list = new ArrayList<Integer>();
        for (int i = 0; i < n; i++) {
            list.add(sc.nextInt());
        }
        int distance = k - list.get(n-1) + list.get(0);
        for (int j = 2; j < n; j++) {
            if (distance < list.get(j) - list.get(j-1)) {
                distance = list.get(j) - list.get(j-1);
            }
        }
        System.out.println(k - distance);
    }
}

/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