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.util.*;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
     Scanner sc=new Scanner(System.in);
     Map<Integer,Integer>map=new HashMap<Integer,Integer>();
     int p=sc.nextInt();
     int n=sc.nextInt();
     for(int i=0;i<n;i++) {
    	 int flag=sc.nextInt()%p;
    	 if(!map.containsValue(flag)) {
    		 map.put(i, flag);
    	 }else {
    		 System.out.println(i+1);
    		 return;
    	 }
     }
     if(map.size()==n) {
    	 System.out.println(-1);
     }
	}

}
