import java.util.*;

public class Main {
    static public void main(String args[]) {

        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        int n = sc.nextInt();
        int firsta = sc.nextInt();
        int prea = firsta, maxdis = 0, nowa = 0;

        for (int i = 0; i < n - 1; i++) {
            nowa = sc.nextInt();
            maxdis = Math.max(maxdis, nowa - prea);
            prea = nowa;
        }

        maxdis = Math.max(maxdis, firsta + k - nowa);

        System.out.println(k - maxdis);

    }
}
/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