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;
import java.math.MathContext;
import java.math.RoundingMode;
public class Test_Data {

 private static final Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {
        double a = scanner.nextInt();
        double b = scanner.nextInt();
        String  c = scanner.next();
        BigDecimal x = new BigDecimal(a);
        BigDecimal y = new BigDecimal(b);
        BigDecimal z = x.divide(y, 1000 /* or Integer.MAX_VALUE */, RoundingMode.HALF_UP);
        String  testof ;
        testof=z.toString();
        String newtest = testof.replaceFirst("0","a");
        int index_c = newtest.indexOf(c);
        if (index_c > 999 ) {
            System.out.println(-1);
        } else if (index_c == -1 ) {
            System.out.println(-1);
        } else {
            System.out.println(index_c-1);
        }
    }
}