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.text.DecimalFormat;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;



public class PositioninFraction1 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
        MyScanner input = new MyScanner();
        
        int a = input.nextInt();
        int b = input.nextInt();
        int c = input.nextInt();
        
        for(int i=1;i<=b;i++){
        	if(a*10/b ==c){
        		System.out.println(i);
        		return;
        	}
        	a = (a*10)%b;
        }
        System.out.println(-1);
        
	}
	

	static class MyScanner {
			BufferedReader br;
			StringTokenizer st;
			public MyScanner() {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
			String next() {while (st == null || !st.hasMoreElements()) {
				try {st = new StringTokenizer(br.readLine());}
				catch (IOException e) {e.printStackTrace();}}
			return st.nextToken();}
			int nextInt() {return Integer.parseInt(next());}
			long nextLong() {return Long.parseLong(next());}
			double nextDouble() {return Double.parseDouble(next());}
			String nextLine(){String str = "";
			try {str = br.readLine();}
			catch (IOException e) {e.printStackTrace();}
			return str;}
		}

}
