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.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.InputStream;

/**
 *      Created by G.Gekko.
 */

public class Solution {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        Task solver = new Task();
        solver.solve(in, out);

        out.close();
    }
}

class Task {


    public void solve(InputReader in, PrintWriter out) {

        int p = in.nextInt();
        int n = in.nextInt();

        int INF = -10;

        int[] a = new int[p+1];
        for (int i = 0; i <= p; i++)
            a[i] = INF;

        for (int i = 0; i < n; i++) {
            int c = in.nextInt();

            int x = c % p;
            if (a[x] == INF)
                a[x] = x;
            else {
               out.print(i+1);
                return;
            }
        }
        out.print(-1);


    }
}


class Algo {

    int max (int a, int b) {
        if (a > b)
            return a;
        else
            return b;
    }

    int min (int a, int b) {
        if (a < b)
            return a;
        else
            return b;
    }

//    int[] sorte (int[] a) {
//        int[] ans = a;
//        for (int i = 0; i < a.length; i++) {
//            for (int j = i; j > 0; j++) {
//                if (ans[j-1] > ans[j]) {
//                    int temp = ans[j-1];
//                    ans[j-1] = ans[j];
//                    ans[j] = temp;
//                }
//            }
//        }
//        return ans;
//    }

}

/*
 *      Reading
 */

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader (InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }

}









