You have a fraction <image>. You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

Input

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Output

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

Examples

Input

1 2 0


Output

2

Input

2 3 7


Output

-1

Note

The fraction in the first example has the following decimal notation: <image>. The first zero stands on second position.

The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction. 
import itertools as it
import re
from math import *
def rt():
    return raw_input()
def rn():
    return int(raw_input())
def rns():
    return map(int,raw_input().split())


x,y,c=rns()

def digit(x,y,i):
    return int(floor(10 * ((10**(i-1)*x) % y) / y) % 10)
res=False
for i in range(1,1000):
    if c==digit(x,y,i):
        res=True
        break
if res:
    print i
else:
    print -1
