import java.util.*;
class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        int n = sc.nextInt();
        int[] houses = new int[n];
        int prev = sc.nextInt();
        houses[0] = prev;
        int max = 0;
        int sum = 0;
        for (int i = 1; i < n; i++) {
            int place = sc.nextInt();
            int gap = place - prev;
            max = Integer.max(max, gap);
            prev = place;
            sum += gap;
            houses[i] = place;
        }
        int gap = houses[0] + k - houses[n-1];
        max = Integer.max(max, gap);
        sum += gap;
        sum -= max;
        System.out.println(sum);
    }
}

/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