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 __future__ import division
import math

A = list(map(int, input().split()))
a = A[0]
b = A[1]
c = A[2]
# reduce the number to its mod
a %= b

index = 0
# traverse for every decimal places
for i in range(1, b + 1):

    # get every fraction places
    # when (a*10/b)/c
    a = a * 10

    # check if it is equal to
    # the required integer
    if int(a / b) == c:
        index = i
        break

        # mod the number
    a %= b

if index != 0:
    print(index)
else:
    print(-1)