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. 
import java.util.*;

public class B_Position_in_Fraction {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int a = in.nextInt(), b = in.nextInt(), c = in.nextInt();
        a %= b;
        for (int ind = 1; ind <= b; ind++) {
            a *=10;
            if (a / b == c) { System.out.println(ind); return; }
            a%=b;
        }
        System.out.println(-1);
    }
}
