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
import sys
from decimal import *

def main():
  a, b, c = map(int, raw_input().split())
  getcontext().prec = 1000
  s =  str(Decimal(float(a)) / Decimal(float(b)))
  while len(s) < 1000:
    s += "0"
  for i in range(2, len(s) - 1):
    if int(s[i]) == c:
      print i - 1
      return
  print -1


if __name__ == '__main__':
  main()
