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 maxDistance = 0;
      	int newPoint;
      	int lastPoint = sc.nextInt();
      	int firstPoint = lastPoint;
      	int distance;
      	for (int i = 0; i <  n; i++) {
          if (i == n - 1) {
            newPoint = firstPoint + k;
          } else {
          	newPoint = sc.nextInt();
          }
          distance = Math.abs(newPoint - lastPoint);
          lastPoint = newPoint;
          maxDistance = maxDistance < distance ? distance : maxDistance;
        }
      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