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 arr[] = new int[n];
        for(int i=0;i<n;i++){
            arr[i] = sc.nextInt();
        }
        int maxDistance = arr[0]+k-arr[n-1];
        for(int i=1;i<n;i++){
            maxDistance = Math.max(maxDistance,arr[i]-arr[i-1]);
        }
        System.out.println(k-maxDistance);
    }
    
}
/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