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 int maxn = 10005;
long long a, b, c;
int main() {
  ios::sync_with_stdio(0);
  cin >> a >> b >> c;
  int pos = 1;
  bool flag = 0;
  while (pos < 10000000) {
    if (a == 0) {
      if (c == 0) {
        cout << pos << "\n";
        flag = 1;
      }
      break;
    }
    a *= 10;
    int cc = a / b;
    if (cc == c) {
      cout << pos << "\n";
      flag = 1;
      break;
    }
    a = a % b;
    pos++;
  }
  if (!flag) {
    cout << -1 << "\n";
  }
  return 0;
}
