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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class A {

	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		
		int ok = 0;
		a %= b;
		a *= 10;
		
		for(int i=1;i<100000;i++) {
			int now = a / b;
			if(now == c && ok == 0) {
				pw.println(i);
				ok = 1;
			}
			a %= b;
			a *= 10;
		}
		
		if(ok == 0) pw.println(-1);
		
		pw.close();
		sc.close();
	}

}

class FastScanner {
	BufferedReader br;
	StringTokenizer st;

	public FastScanner(InputStream is) {
		br = new BufferedReader(new InputStreamReader(is));
		st = null;
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public void close() throws IOException {
		br.close();
	}
}