
import java.util.Scanner;

public class Main {

	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int k = sc.nextInt();
		int n = sc.nextInt();
		int[] house = new int[n];
		for(int i=0;i<n;i++){
			house[i]=sc.nextInt();
		}
		int maxDist = k-(house[n-1]-house[0]);
		for(int i=0;i<n-1;i++){
			if(house[i+1]-house[i]>maxDist){
				maxDist = house[i+1]-house[i];
			}
		}
		System.out.println(k-maxDist);
	}
}

/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