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
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.Scanner;

/**
 *
 * @author alina
 */
public class DZY {
    public static void main(String[] args) 
    {
        Scanner in = new Scanner(System.in);
        int p = in.nextInt();
        int n = in.nextInt();
        String[] results = new String[p];
        int l= -1;
        
        int x = 0;
        boolean prov = false;
        
        for(int i = 0; i < n; ++i)
        {
            x = in.nextInt();
            int index = x % p;
            if(!prov&& results[index] != null){
                prov= true; l = i + 1;
            }
            
            results[index] = x + "";
            
            
        }
            System.out.println(l);
        
    }
}
