DZY has a hash table with p buckets, numbered from 0 to p - 1. He wants to insert n numbers, in the order they are given, into the hash table. For the i-th number xi, DZY will put it into the bucket numbered h(xi), where h(x) is the hash function. In this problem we will assume, that h(x) = x mod p. Operation a mod b denotes taking a remainder after division a by b.

However, each bucket can contain no more than one element. If DZY wants to insert an number into a bucket which is already filled, we say a "conflict" happens. Suppose the first conflict happens right after the i-th insertion, you should output i. If no conflict happens, just output -1.

Input

The first line contains two integers, p and n (2 ≤ p, n ≤ 300). Then n lines follow. The i-th of them contains an integer xi (0 ≤ xi ≤ 109).

Output

Output a single integer — the answer to the problem.

Examples

Input

10 5
0
21
53
41
53


Output

4


Input

5 5
0
1
2
3
4


Output

-1

import java.util.*;

public class Solving {
    
private static Scanner in =new Scanner(System.in);

 public static void main(String[] args){
     HashMap<String,Integer> map=new HashMap<String,Integer>();
     int p=in.nextInt();
     int n=in.nextInt();
     int index=-1;
     for(int i=0;i<n;i++){
         int cur=in.nextInt();
         String key=String.valueOf(cur%p);
         if(map.containsKey(key)){
                 index=i+1;
                 break;
             }
         else{
             map.put(key,cur);
         }
     }
     System.out.println(index);
 }
}