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.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.util.TreeMap;
import java.util.TreeSet;


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		
		int p = sc.nextInt();
		int n = sc.nextInt();
		int[] h = new int[p];
		int ans = -1;
		for (int i=0; i < n;i++) {
			int x = sc.nextInt();
			if (h[x%p] == 0) {
				h[x%p] = 1;
			}else {
				ans = i+1;
				break;
			}
		}
		
		//TreeSet<Character> ts = new TreeSet();
		//TreeMap<Integer,Integer> tm = new TreeMap<Integer,Integer>();
		//ArrayList<ArrayList<Integer>> tubes = new ArrayList<ArrayList<Integer>>();
		//ArrayList<Integer[]> al = new ArrayList<Integer[]>();
		
		System.out.println(ans);
		
	}









}
