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
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.Scanner;

/**
 *
 * @author Nurlybek
 */
public class HashCode {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        
        int k = in.nextInt();
        int n = in.nextInt();
        
        int cell[] = new int[301];
        int ans = -1;
        
        for(int i = 0; i < n; i++) {
            
            int x = in.nextInt();
            x %= k;
            
            if(cell[x] == 0) {
                cell[x] = 1;
                continue;
            }
            else {
                if(ans == -1) {
                    ans = i;
                }
            }
        }
        if(ans != -1) {
            System.out.println(ans+1);
        }
        else {
            System.out.println("-1");
        }
    }
}
