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.BigInteger;
import java.util.*;
public class Main {
	private static Scanner cin;
	public static void main(String[] args) {
		cin = new Scanner(System.in);
		double a=cin.nextDouble();
		double b=cin.nextDouble();
		int c=cin.nextInt();
		String t1=Double.toString(a);
		String t2=Double.toString(b);
		BigDecimal tt1=new BigDecimal(t1);
		BigDecimal tt2=new BigDecimal(t2);
		BigDecimal ans=tt1.divide(tt2, 10000, BigDecimal.ROUND_HALF_UP);
		int flag=0,index=0;
		String res=ans.toString();
		for(int i=2;i<=10000;i++) {
			if(res.charAt(i)-'0'==c) {
				flag=1;
				index=i;
				break;
			}
		}
		if(flag==1) System.out.println(index-1);
		else System.out.println(-1);
	}
}
