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.*;
import java.io.*;
import java.math.*;

public class test{
	

	  public static void main(String[] args) throws IOException {
	  Scanner sc=new Scanner(System.in);
		int aa=sc.nextInt();
		int bb=sc.nextInt();
		int cc=sc.nextInt();
		
		


		BigDecimal a1=new BigDecimal(aa+"");
		BigDecimal b1=new BigDecimal(bb+"");

		BigDecimal bc=a1.divide(b1,100006,RoundingMode.FLOOR);


		String str=bc.toString();
		int index1=str.indexOf('.');
		String cop=str.substring(index1,str.length());

		int answer=cop.indexOf((char)(48+cc));
		if(answer==1000006){
			answer=-1;
		}
		System.out.println(""+answer);
		
	}
}