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[] A = new int[N];
		for (int i = 0; i < N ; i++) A[i] = sc.nextInt();
		int max = (K - A[N-1]) + A[0];
		for (int i = 0; i < A.length; i++) {
			if (i == 0) continue;
			else {
				int m = A[i] - A[i-1];
				if (max < m) max = m;
			}
		}
		System.out.println(K - max);
	}
}
/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