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.*;
import java.io.*;
import java.util.Collections;

public class Solution {

    static class Solver {

        Solver() {
        }

        public void solve(FastScanner sc, PrintWriter out) throws IOException {
            int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt();
            for(int i = 1; i <= b; i++) {
                a *= 10;
                if(a/b == c) {
                    System.out.println(i);
                    return;
                }
                a %= b;
            }
            out.println(-1);
        }

    }
    public static void main(String[] args) throws IOException{
        FastScanner scanner = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        (new Solver()).solve(scanner, out);
        out.flush();

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        boolean hasNextToken() {
            if(st == null) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(IOException e) {

                }
            }
            return st.hasMoreTokens();
        }

        String next() {
            while(st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(IOException e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

        String nextLine() throws IOException{
            return br.readLine();
        }

        byte nextByte() {
            return Byte.parseByte(next());
        }

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

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

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