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.BufferedReader;
import java.io.IOError;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
	public static void main(String[] args) throws IOException {

		BufferedReader reader = new BufferedReader(new InputStreamReader(
				System.in));
		String[] strings = reader.readLine().split(" ");
		int p = Integer.valueOf(strings[0]);
		int n = Integer.valueOf(strings[1]);
		ArrayList<Long> list = new ArrayList<Long>();
		ArrayList<Long> integers = new ArrayList<Long>();
		int iterationNumber = 1;
		while (n-- > 0) {
			integers.add(Long.valueOf(reader.readLine()));
		}
		for (Long integer : integers) {
			// System.out.println(integer % p);
			if (list.isEmpty()) {
				list.add(integer % p);
				iterationNumber++;
				continue;
			}
			if (list.contains(integer % p)) {
				System.out.println(iterationNumber);
				return;
			}
			list.add(integer % p);
			iterationNumber++;
		}

		System.out.println(-1);

	}
}
