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;
string s;
int main() {
  int n, m;
  char k;
  cin >> n >> m >> k;
  for (int i = 1; i <= 10000000; i++) {
    int x = n * 10 / m;
    char y = x + '0';
    s += y;
    n *= 10;
    n -= x * m;
    if (n == 0) {
      s += '0';
      break;
    }
  }
  bool flag = false;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == k) {
      flag = true;
      cout << i + 1 << endl;
      break;
    }
  }
  if (!flag) cout << -1 << endl;
  return 0;
}
