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;
const long double eps = 1e-9;
const double EPS = 1e-9;
int ar[] = {1, -1, 0, 0, 1, 1, -1, -1};
int ac[] = {0, 0, 1, -1, 1, -1, 1, -1};
int main() {
  ios_base::sync_with_stdio(false);
  int a, b, c;
  cin >> a >> b >> c;
  int cnt = 2000;
  for (int i = 1; i <= cnt; i++) {
    a *= 10;
    if (a < b) {
      if (c == 0) return cout << i << "\n", 0;
      while (a > 0 && a < b) {
        a *= 10;
        i++;
      }
    }
    if (c == a / b) return cout << i << "\n", 0;
    a %= b;
  }
  cout << "-1\n";
  return 0;
}
