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.*;
import java.util.*;

public class PositionInFraction {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		BigDecimal a=new BigDecimal(scan.nextInt()), b=new BigDecimal(scan.nextInt());
		int c=scan.nextInt();
		
		String s=""+a.divide(b,1000,RoundingMode.DOWN);
		s=s.substring(2);
		
		int x=s.indexOf(c+"");
		//omg
		System.out.println(x==-1?-1:(x+1));
	}
}