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.math.*;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		BigDecimal a = in.nextBigDecimal();
		BigDecimal b = in.nextBigDecimal();
		int c = in.nextInt();
		BigDecimal res = a.divide(b, 100000, BigDecimal.ROUND_HALF_UP);
		res = res.setScale(100000, BigDecimal.ROUND_HALF_UP);
		String s = res.toString();
		int idx = s.indexOf(".");
		s = s.substring(idx+1);
		char ch[] = s.toCharArray();
		int ans = -1;
		for(int i=0; i<ch.length-1; ++i) {
			if(ch[i]-'0' == c) {
				ans = i+1;
				break;
			}
		}
		System.out.println(ans);
	}
}