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 math as Math
n,m,k=[int(i) for i in raw_input().split()]
count=0
flag=True
#Numerator is multiplied 10 times
while(count<=10000):
    n=n*10
    count=count+1
    if k==(n/m)%10:
        flag=False
        break
if flag:
    print -1
else:
    print count