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.ArrayList;
import java.util.Collections;

import java.util.Scanner;


/**
 *
 * @author ������
 */
public class JavaClass {
    public static void main(String[] args)
    {
Scanner in=new Scanner(System.in);
int a=in.nextInt();
int b=in.nextInt();
int c=in.nextInt();
int count=0;
boolean yeap=false;
int e=a%b;
while(a!=0)
{ a=(a%b)*10;
  int x=a/b;

count++;
if ((c==x)&&(count>0)) {yeap=true;break;}
if ((a==0)&&(c==0)) {yeap=true;count++;break;}


if (a%b==e) break;
}
if (yeap)
System.out.println(count);
else System.out.println(-1);
    }}
    
