Problem2752--DZY Loves Hash

2752: DZY Loves Hash

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
[Submit] [Status] [Web Board] [Creator:]

Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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)=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.

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

Source/Category