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.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;
import java.io.InputStream;
import java.io.InputStreamReader;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int p=in.nextInt();
        int n = in.nextInt();

        boolean[] a = new boolean[p];

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

            if (a[x % p]){
                out.println(i+1);
                return;
            }

            a[x % p] = true;
        }
        
        out.println(-1);
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;


    public InputReader(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
    }

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

        return tokenizer.nextToken();
    }

    public int nextInt(){
        return Integer.valueOf(next());
    }

}

