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.InputStreamReader;
import java.util.HashSet;

public class CFTest143 {

	static BufferedReader br;

	public static void main(String[] args) {
		br = new BufferedReader(new InputStreamReader(System.in));

		try {

			int[]arr=readIntArr();
			int p=arr[0];
			int n=arr[1];
			HashSet<Integer>hs=new HashSet<Integer>();
			
			for(int i=0;i<n;i++){
				int bkt=readInt()%p;
				if(hs.contains(bkt)){
					System.out.println(i+1);
					br.close();
					return;
				}
				hs.add(bkt);
			}
			
			System.out.println(-1);
			br.close();

		} catch (IOException e) {
			e.printStackTrace();
		}

	}

	static public String readLine() throws IOException {
		return br.readLine();

	}

	static public String readString() throws IOException {
		return br.readLine();

	}

	static public long readlong() throws IOException {
		return Long.parseLong(br.readLine());
	}

	static public int readInt() throws IOException {
		return Integer.parseInt(br.readLine());
	}

	static public int[] readIntArr() throws IOException {
		String[] str = br.readLine().split(" ");
		int arr[] = new int[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Integer.parseInt(str[i]);
		return arr;
	}

	static public double[] readDoubleArr() throws IOException {
		String[] str = br.readLine().split(" ");
		double arr[] = new double[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Double.parseDouble(str[i]);
		return arr;
	}

	static public long[] readLongArr() throws IOException {
		String[] str = br.readLine().split(" ");
		long arr[] = new long[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Long.parseLong(str[i]);
		return arr;
	}

	static public double readDouble() throws IOException {
		return Double.parseDouble(br.readLine());
	}
}
