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 A1008 {
    public static void main(String [] args) {
        InputStream inputReader = System.in;
        OutputStream outputReader = System.out;
        InputReader in = new InputReader(inputReader);
        PrintWriter out = new PrintWriter(outputReader);
        Algorithm solver = new Algorithm();
        solver.solve(in, out);
        out.close();
    }
}

class Algorithm {
    void solve(InputReader ir, PrintWriter pw) {

        int p = ir.nextInt(), n = ir.nextInt(), num = -1;
        int [] x = new int[p];

        for (int i = 0, pos; i < n; i++) {
            pos = ir.nextInt() % p;
            if (x[pos] == 0) x[pos] = 1;
            else {
                num = i + 1;
                break;
            }
        }
        pw.print(num);

    }

    private static void Qsort(int[] array, int low, int high) {

        int i = low;
        int j = high;
        int x = array[low + (high - low) / 2];

        do {
            while (array[i] < x) ++i;
            while (array[j] > x) --j;
            if (i <= j) {
                int tmp = array[i];
                array[i] = array[j];
                array[j] = tmp;
                i++;
                j--;
            }
        } while (i <= j);

        if (low < j) Qsort(array, low, j);
        if (i < high) Qsort(array, i, high);

    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

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

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

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

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

}