import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int k  = Integer.parseInt(scanner.next());
        int n  = Integer.parseInt(scanner.next());
        int[] a = new int[n];
        int cost;
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(scanner.next());
        }
        cost = k - Math.abs(k - a[n-1] + a[0]);
        for (int i = 1; i < n; i++) {
            cost = Math.min(cost, k - Math.abs(a[i] - a[i-1]));
        }
        System.out.println(cost);
        
    }
}

/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