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.*;
import java.math.*;
public class j {
	public static long pow(int n) {
		long p = 1;
		while(n-->0) {
			p*=2;
		}
		return p;
	}
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner sc = new Scanner(System.in);
		String[] str = br.readLine().split(" ");
		int a = Integer.parseInt(str[0]);
		int b = Integer.parseInt(str[1]);
		int c = Integer.parseInt(str[2]);
		int[] v = new int[100005];
		int count_position =0 ;
		v[0] = 1;
		while(true) {
			count_position++;
			if(v[a]!=0) {//if a==0
				if(a==0) {
					if(c==0) {
						System.out.println(count_position);
						break;
					}
				}
				System.out.println(-1);break;
			}
			v[a] = count_position;
			if(c == a*10/b) {
				System.out.println(count_position);
				break;
			}
			a = a*10%b;
		}
	}
}