You have a fraction . 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.

Note

The fraction in the first example has the following decimal notation: . The first zero stands on second position.

The fraction in the second example has the following decimal notation: . There is no digit $7$ in decimal notation of the fraction.