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
Copy
10 5
0
21
53
41
53
Output
Copy
4
Input
Copy
5 5
0
1
2
3
4
Output
Copy
-1
就是问hash是否存在冲突;
用 map 去判重即可;
当然开数组也没问题;
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EPFL - Fighting