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 ≤ 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.

见题面 Input 部分

见题面 Output 部分

The fraction in the first example has the following decimal notation: $${ \frac { 1 } { 2 } } = 0. 5 0 0 ( 0 )$$. The first zero stands on second position.

The fraction in the second example has the following decimal notation: $${ \frac { 2 } { 3 } } = 0. 6 6 6 ( 6 )$$. There is no digit 7 in decimal notation of the fraction.