You have a fraction $\frac{a}{b}$. 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 ≤ 10^5, 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: $\frac{1}{2} = 0.500(0)$. The first zero stands on second position.

The fraction in the second example has the following decimal notation: $\frac{2}{3} = 0.666(6)$. There is no digit 7 in decimal notation of the fraction.