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
# coding: utf-8

import os
from sys import stdin
from itertools import imap

DEBUG = False

def input_lines():
    if DEBUG:
    	file_name = os.path.join(os.getcwd(), 'input.txt')
        with open(file_name, 'r') as input_file:
            for line in input_file:
                yield line

    else:
        for line in stdin:
            yield line


def hash(x, p):
    """
    h(x) = x mod p
    """
    return x % p


class InputLine(object):

    def __init__(self, array, n):
        self._x_array = [int(x) for i, x in enumerate(array) if  i < n]

    def __iter__(self):        
        for x in self._x_array:
            yield x


class HashTable(object):

    def __init__(self, p):
        self._table = dict()
        self._p = p

    def setitem(self, x):
        index = hash(x, self._p)
        collision = index in self._table
        self._table[index] = x

        return collision


def main(input_generator):
    p, n = map(int, input_generator.next().split(' '))

    i_lines = InputLine(input_generator, n)
    hash_table = HashTable(p)

    for i, x in enumerate(i_lines, start=1):
        collision = hash_table.setitem(x)
        if collision:
            print i
            break
    else:
        print -1


if __name__ == '__main__':
    main(input_generator=input_lines())