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 = map(int, input().split(' '))
getcontext().prec = 10000
s = str(Decimal(a) / Decimal(b))
s += '0'
l = s.split('.')

if l[1].find(str(c)[0]) < 9000 and l[1].find(str(c)[0]) != -1:
  print(l[1].find(str(c)[0]) + 1)
else:
  print(-1)