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 rps(List, aranan):

    if aranan in List:
        return True

    return False


sayi1, sayi2 = [int(x) for x in raw_input().split(" ")]

bool = False
sayi1 = int(sayi1)
sayi2 = int(sayi2)

myList = [int(temp) for temp in range(sayi2)]
myListMode = [int(temp) for temp in range(sayi2)]
for s in range(len(myListMode)):
    myListMode[s] = sayi1




for a in range(sayi2):
    number = raw_input()
    myList[a] = int(number)

i = 0
m = 0
sTemp = 0

while i < sayi2:
    sTemp = myList[i]
    hasha = sTemp % sayi1
    if rps(myListMode,hasha):
        bool = True
        m = i
        i = sayi2
    else:
        myListMode[i] = hasha
        i += 1



m += 1
if bool:
    print m
else:
    print -1