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 = 500

split_strings = input().split()
[a, b, c] = map(lambda x: int(x), split_strings)

a = Decimal(a)
b = Decimal(b)

decimal = (a / b) * 10


for i in range(1, 500):
    ones = int(decimal)
    fractional = decimal % 1

    if ones == c:
        print(i)
        exit()
    
    decimal = fractional * 10


print(-1)

