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.*;

public class Main
{
    static int[] A;
    public static void main(String args[]) throws java.lang.Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String[] s=br.readLine().split(" ");
        int P=Integer.parseInt(s[0]);
        int N=Integer.parseInt(s[1]);

        int[] A=new int[P];
        int print=-1,t=0,f=0;
        boolean enter=true;
        for(int i=0;i<N;i++)
        {
            t=Integer.parseInt(br.readLine());
            if(A[f=t%P]!=0&&enter)
            {
                print=i+1;
                enter=false;
            }
            else
            A[f]=1;
        }
        System.out.println(print);
    }   

}