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.io.*;
import java.util.*;


public class Main {

	public static class pair implements Comparable<pair>
	{
		int a;
		int b;
		public pair(int pa, int pb)
		{
			a = pa; b= pb;
		}
		@Override
		public int compareTo(pair o) {
			if(this.a < o.a)
				return -1;
			if(this.a > o.a)
				return 1;
			return Integer.compare(o.b, this.b);
		}
	}

	//int n = Integer.parseInt(in.readLine());
	//String[] spl = in.readLine().split(" ");


	public static void main (String[] args) throws Exception
	{	
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] spl = in.readLine().split(" ");
		int p = Integer.parseInt(spl[0]);
		int n = Integer.parseInt(spl[1]);
		boolean[] taken = new boolean[p];
		boolean fin  = false;
		for (int i = 0; i < n; i++) {
			int c = Integer.parseInt(in.readLine());
			int mod = c%p;
			if(taken[mod])
			{
				System.out.println(i+1);
				fin = true;
				break;
			}
			taken[mod]=true;
		}
		if(!fin)
			System.out.println(-1);
	}
}