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.IOException;
import java.util.StringTokenizer;

public final class Main {
    static String ReadLn(int maxLg) {
        byte lin[] = new byte[maxLg];
        int lg = 0, car = -1;

        try {
            while (lg < maxLg) {
                car = System.in.read();
                if ((car < 0) || (car == '\n'))
                    break;
                lin[lg++] += car;
            }
        } catch (IOException e) {
            return (null);
        }

        if ((car < 0) && (lg == 0))
            return (null);
        return (new String(lin, 0, lg));
    }

    public static void main(String args[]) {
        Main myWork = new Main();
        myWork.Begin();
    }

    void Begin() {

        int p;
        int n;
        int[] buckets;
        int[] hash;
        int result = -2;

        String firstLine = Main.ReadLn(255);
        StringTokenizer st = new StringTokenizer(firstLine);

        p = Integer.parseInt(st.nextToken());
        n = Integer.parseInt(st.nextToken());
        buckets = new int[n];
        hash = new int[p];

        for (int i = 0; i < n; i++) {
            String bucket = Main.ReadLn(255).trim();
            buckets[i] = Integer.parseInt(bucket);
        }

        for (int i = 0; i < p; i++) {
            hash[i] = -1;
        }

        for (int i = 0; i < n; i++) {
            int func = buckets[i] % p;
            if (hash[func] != -1) {
                result = i;
                break;
            } else {
                hash[func] = buckets[i];
            }
        }
        System.out.println(++result);

    }
}