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 fractions import Fraction

(a, b, c) = tuple(map(int, input().split()))
f = Fraction(a, b)
for i in range(900):
    for j in range(10):
        if f < Fraction(j+1, 10):
            if j == c:
                print(i+1)
                exit(0)
            f -= Fraction(j, 10)
            f *= 10
            break
print(-1)
