import java.util.*;

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

        int[] distances = new int[N];

        for (int i = 0; i < N; i++) {
            distances[i] = stdIn.nextInt();
        }

        stdIn.close();

        int max = distances[0] + K - distances[N-1];
        for (int i = 0; i < N-1; i++) {
            if (max < distances[i+1] - distances[i]) {
                max = distances[i+1] - distances[i];
            }
        }

        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