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
n,m = map(int, input() .split())
x = []
t = [-1]*m
j = 0
c= False
for i in range(m):
  x += list(map(int , input() .split()))
for k in range(m):
  t[j] = x[k] % n
  j+=1
for l in range(m):
  for y in range(0,l): 
    if l!=y:
      if t[l] == t[y]:
        c = True
        print(l+1)
        exit()      
if c == False:
  print(-1) 