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