import java.io.IOException;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        Scanner in = new Scanner(System.in);
        int k = in.nextInt();
        int n = in.nextInt();
        int[] arr = new int[n];
        int[] ans = new int[n];

        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        for (int i = 1; i < n; i++) {
            ans[i] = arr[i] - arr[i - 1];
        }
        ans[0] = k - arr[n - 1] + arr[0];

        int temp = 0;
        for (int i = 1; i < n; i++) {
            if (Math.max(ans[temp], ans[i]) == ans[i]) {
                temp = i;
            }
        }
        System.out.println(k - ans[temp]);
    }
}
/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