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 *
getcontext().prec = 2048
getcontext().rounding = ROUND_DOWN
num, denom, target = [int(x) for x in input().split()]
a = Decimal(num)/Decimal(denom)
a = str(a)
a = a[a.find('.') : ]
if len(a) < 2047:
    a = a + '0'
print(a.find(str(target)))
