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 sys
import decimal

def main():
    lim = 10000
    decimal.getcontext().prec = lim
    
    a, b, c = map(int, raw_input().split())
    x = decimal.Decimal(a) / decimal.Decimal(b)
    s = str(x)
    
    if len(s) != (lim + 2):
	s = s + "0"
    
    pos = s.find(chr(c + 48), 1)
    if pos >= lim:
	pos = -1
    print max(-1, pos - 1)
    
if __name__ == '__main__':
    main()
