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.RoundingMode;
import java.util.*;

public class R450B {
	
	static boolean[] seen = new boolean[100];

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int a = scan.nextInt();
		int b = scan.nextInt();
		int c = scan.nextInt();
		int scale = (int)(1e5+200);
		BigDecimal num1 = new BigDecimal(a);
		BigDecimal num2 = new BigDecimal(b);
		String s = num1.divide(num2, scale, RoundingMode.UP).toString();
		for(int i = 2; i < s.length()-1; i++){
			if(s.charAt(i)-'0' == c){
				System.out.println(i-1);
				return;
			}
		}
		System.out.println(-1);
	}
}
