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. 
// Codeforces 900.2
import java.util.*;

public class Position {
	public static void main(String[] args) {
		Scanner f = new Scanner(System.in);
		int a = f.nextInt(), b = f.nextInt(), c = f.nextInt(), remainder = 0;
		a = a % b;
		for (int i = 1; i <= b; i++) {	//We definitely start repeating after b digits.
			a *= 10;
			if (a / b == c) {
				System.out.println(i);
				System.exit(0);
			}
			a %= b;
		}
		System.out.println(-1);
	}
}
