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

public class B900 {
	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader in = new BufferedReader(new FileReader("cf.in"));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

		StringTokenizer st = new StringTokenizer(in.readLine());
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		int c = Integer.parseInt(st.nextToken());

		boolean found = false;

		for (int i = 1; i <= b; i++) {
			a *= 10;
			if (a / b == c) {
				out.println(i);
				found = true;
				break;
			}
			a %= b;
		}

		if (!found) out.println(-1);

		out.close();
	}
}
