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)=xmodp. Operation amodb 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.

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 x_i (0≤x_i≤10⁹).

Output a single integer − the answer to the problem.