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

public class DZYLovesHashes {

    public void solve(InputReader reader) {
        int p = reader.nextInt();
        int n = reader.nextInt();

        int[] x = new int[n];
        boolean[] hs = new boolean[p];
        for (int i = 0; i < n; i++)
            x[i] = reader.nextInt();

        for (int i = 0; i < n; i++) {
            int h = x[i] % p;
            if (hs[h]) {
                System.out.println(i + 1);
                return;
            }
            hs[h] = true;
        }

        System.out.println(-1);
    }

    public static void main(String[] s) {
        try (InputReader reader = new InputReader(System.in)) {

            DZYLovesHashes h = new DZYLovesHashes();
            h.solve(reader);
        }
    }

    public static class InputReader implements AutoCloseable {

        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public InputReader(InputStream in) {
            assert in != null;
            reader = new BufferedReader(new InputStreamReader(in), Short.MAX_VALUE);
        }

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

        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = null;
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            } else {
                StringBuilder builder = new StringBuilder();
                while (tokenizer.hasMoreTokens()) {
                    builder.append(tokenizer.nextToken());
                    builder.append(' ');
                }
                return builder.toString();
            }
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public void close() {
            try {
                reader.close();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}
