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>
namespace patch {
template <typename T>
std::string to_string(const T& n) {
  std::ostringstream stm;
  stm << n;
  return stm.str();
}
}  // namespace patch
using namespace std;
int main() {
  map<int, bool> chk;
  long long A, B, C;
  cin >> A >> B >> C;
  long long cn = 0;
  while (1) {
    if (chk[A]) {
      break;
    }
    chk[A] = true;
    cn++;
    A *= 10;
    long long dig = A / B;
    if (dig == C) {
      cout << cn;
      return 0;
    }
    A %= B;
  }
  cout << -1;
  return 0;
}
