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 decimal import * 
a,b,c=[int(i)for i in input().split()]
getcontext().prec = 1000
x = Decimal(a)
y = Decimal(b)
s=str(x/y)
if len(s) >1000 :h = s[2:-1].find(str(c))
else : h = s[2:].find(str(c))
if c == 0 and h == -1 and len(s)<1000:print(len(s)-1)
else : print(  h + 1 if h != -1 else -1)