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
def main():
    (p, nlines) = map(int, raw_input().split())

    nums = [0] * p
    first_pos = -1
    i = 0

    while i < nlines:
        num = int(raw_input())
        if nums[num % p]:
            if first_pos == -1:
                first_pos = i+1
        
        else:
            nums[num % p] = 1
        
        i += 1
    
    if first_pos != -1:
        print first_pos
    else:
        print '-1'

    return


if __name__ == '__main__':
    main()
