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 x i , DZY will put it into the bucket numbered h(x i ), 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.

输入描述:

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).

输出描述:

Output a single integer — the answer to the problem.