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.io.*;
import java.util.*;

public class Div2_450 {
	
	public static void main(String args[]) throws Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String ip[] = br.readLine().split( " ");
		int a = Integer.parseInt(ip[0]);
		int b = Integer.parseInt(ip[1]);
		int c = Integer.parseInt(ip[2]);
		HashSet<Integer> setOfDigits =  new HashSet<>();
		int rem = a%b,val,pos = 1;
		boolean flag = false;
		if(c == 0 && rem == 0)
		{
			flag = true;
		}
		while(rem != 0 && !setOfDigits.contains(rem) && !flag)
		{
			setOfDigits.add(rem);
			val = (rem * 10)/b;
			rem = (rem*10)%b;
			if(val == c)
			{
				flag = true;
				break; 
			}
			if(rem == 0 && c == 0)
			{
				flag = true;
				pos++;
				break;
			}
			
			pos++;
		}
		if(flag)
			System.out.println(pos);
		else
			System.out.println(-1);
	}
}
