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.Scanner;
public class DZY447A
{
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		int  p = sc.nextInt();
		int n = sc.nextInt();	
		int a[] =new int[n];
		int k=0;
		int t=0;
		for(int i=0;i<n;i++)
		{
			a[i] = sc.nextInt();
		}
		int i=0,l=0;
		for(i=0;i<n;i++)
		{
			k = a[i]%p;
			for(int j=i-1;j>=0;j--)
			{
				if(k==a[j]%p)
				{	t++;
				}
			}
			if(t>0)
			{	l=1;
				break;
			}
		}
		if(l==1)
		System.out.println(i+1);
		else
		System.out.println("-1");

	}
}