//Referred Professors code
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
 
public class Main {
	
	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int k = Integer.parseInt(st.nextToken());
		int n = Integer.parseInt(st.nextToken());
		int[] aa = new int[n];
		st = new StringTokenizer(br.readLine());
		for (int i=0; i<n; i++)
			aa[i] = Integer.parseInt(st.nextToken());
		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