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.BufferedInputStream;
import java.io.FileReader;
import java.math.BigDecimal;
import java.util.Scanner;

import javax.script.ScriptEngine;
import javax.script.ScriptEngineManager;
import javax.script.ScriptException;

public class Main {

	public static void main(String args[]) {
		Scanner cin = new Scanner(new BufferedInputStream(System.in));
		BigDecimal a = cin.nextBigDecimal();
		BigDecimal b = cin.nextBigDecimal();
		int c = cin.nextInt();
		a = a.divide(b, 100000, BigDecimal.ROUND_CEILING);
		String str = a.toString();

		// str = "121.0000";
//		System.out.println(str);

//		String[] strs = str.split("\\.");

//		for (String au : strs) {
//			System.out.println(au);
//		}

		str = str.split("\\.")[1];
//		System.out.println(str);
		
		for (int i = 0; i < str.length() - 100; i++) {
			if (str.charAt(i) == c + '0') {
				System.out.println(i + 1);
				return;
			}
		}
		System.out.println(-1);
	}
}
