import java.util.Scanner;

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

		Scanner scanner = new Scanner(System.in);

		String[] tmp = scanner.nextLine().split(" ");
		Long k 	     = Long.parseLong(tmp[0]);
		int  n 	     = Integer.parseInt(tmp[1]);

		String[] tp  = scanner.nextLine().split(" ");
		long[] list  = new long[n];
		for(int i = 0; i < n; i++) list[i] = Long.parseLong(tp[i]);

		long ans = 0;

		for(int j = 0; j < n; j++) {

			if(j != n - 1) ans = Math.max(ans, list[j + 1] - list[j]);
			else ans = Math.max(ans, Math.abs(list[0] +  (k- list[j])));


		}

		System.out.println(k - ans);



	}
}
/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