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. 
#include <bits/stdc++.h>
using namespace std;
int main() {
  int a, b, c;
  while (cin >> a >> b >> c) {
    int t = 10000;
    int cnt = 1;
    bool flag = false;
    while (t--) {
      int temp = a * 10 / b;
      if (temp == c) {
        cout << cnt << endl;
        flag = true;
        break;
      }
      a = a * 10 % b;
      cnt++;
    }
    if (!flag) cout << -1 << endl;
  }
  return 0;
}
