//Referred Professors code
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[] aa = new int[n];
		for (int i=0; i<n; i++)
			aa[i] = sc.nextInt();
		int gap = aa[0] + k - aa[n-1];
		for (int i = 1; i < n; i++)
			gap = Math.max(gap, aa[i]-aa[i-1]);
		System.out.println(k-gap);
	}
}
/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