import java.util.*;
import java.lang.*;
import java.io.*;
 
public class Main {
    public static void main(String args[]) {
		 Scanner sc = new Scanner(System.in);
		 int k = sc.nextInt();
		 int n = sc.nextInt();
		 int iBefore = sc.nextInt();
		 int i0 = iBefore;
		 int max = Integer.MIN_VALUE;
		 int in = 0;
		 for (int j = 1; j<n ; j++) {
			in = sc.nextInt();
			max = Math.max(max,in - iBefore);
			iBefore = in;
		 }
		 System.out.println(k - Math.max(max,k - in + i0));
	}
}
/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