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. 
from sys import stdin, stdout
from decimal import *

getcontext().prec = 1000

a,b,c = map(int,stdin.readline().rstrip().split())
x = str(Decimal(a)/Decimal(b))[2:]

if len(x)==1000:
    x=x[:-1]
else:
    x = ''.join([x,'0'])
    
if str(c) in x:
    print(x.index(str(c))+1)
else:
    print(-1)

