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.math.BigDecimal;
import java.util.Scanner;

public class Main {
    static public void main(String agrs[]) {
        Scanner cin = new Scanner(System.in);
        BigDecimal a, b;
        String k;
        a = cin.nextBigDecimal();
        b = cin.nextBigDecimal();
        k = cin.next();
        a = a.divide(b, 500, BigDecimal.ROUND_HALF_UP);
        String ans = a.toPlainString();
        ans = ans.substring(ans.indexOf('.'));
        int pos = ans.indexOf(k.charAt(0));
        if (pos == 500) pos = -1;
        System.out.println(pos);
    }
}