import java.util.*;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        Scanner itr = new Scanner(System.in);
        int K = itr.nextInt();
        int N = itr.nextInt();
        int[] place = new int[N];

        for (int i = 0; i < N; i++) {
            place[i] = itr.nextInt();
        }
        Arrays.sort(place);
        int max = K - place[N - 1] + place[0];
        for (int i = 1; i < N; i++) {
            max = Math.max(max, place[i] - place[i - 1]);
        }

        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