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 arcD {
	public static void main(String[] args) {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out);
		
		int a=sc.nextInt();
		int b=sc.nextInt();
		int c=sc.nextInt();
		
		int ans=-1;
		for(int i=0;i<1e6;i++){
			a*=10;
			int x=a/b;
			if(x==c){
				ans=i+1;
				break;
			}
			a%=b;
		}
		pw.println(ans);
		
		pw.flush();
		pw.close();
	}
	
	static class MyScanner{
		BufferedReader br;
		StringTokenizer st;
		
		MyScanner(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		String next(){
			while(st==null || !st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
	}
}
