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.math.RoundingMode;
import java.util.Scanner;

/**
 * Created by Abid on 11/12/2017.
 */
public class Main {

    public static void main(String[] args) {
        int scale = 10000;

        boolean isFound = false;

        Scanner myScanner = new Scanner(System.in);

        double input1 = myScanner.nextDouble();
        double input2 = myScanner.nextDouble();
        char c = myScanner.next().charAt(0);


        BigDecimal num1 = new BigDecimal(input1);
        BigDecimal num2 = new BigDecimal(input2);
        String result = (num1.divide(num2, scale, RoundingMode.HALF_UP).toString());

        //System.out.println(c);
        //System.out.println(result);

        char[] ch= result.toCharArray();

        int pos = 0;

        for(int i =0;i<scale-1; i++){
            if(ch[i] == '.'){
                pos = i;
                break;
            }
        }

        int count = 1;

        for(int i = pos+1;i<scale-1; i++){
            if(ch[i] == c){
                System.out.println(count);
                isFound = true;
                break;
            }
            count++;
        }

        if(isFound==false){
            System.out.println(-1);
        }


    }
}
