import java.util.*;

public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		long K = scan.nextLong();
		int N = scan.nextInt();
		long [] house = new long[N + 1];
		long l = 0;

		for(int i=0; i < N; i++){
			house[i] = scan.nextLong();
		}
		house[N] = K + house[0];

		for(int i=0; i < N; i++){
			if (l < (house[i+1] - house[i]) )l = (house[i+1] - house[i]);
		}

		System.out.println(K - l);
	}
}
/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