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>
#pragma GCC optimize("03")
using namespace std;
template <typename A, typename B>
ostream &operator<<(ostream &out, pair<A, B> &a) {
  return out << "(" << a.first << ", " << a.second << ")\n";
}
template <typename A>
ostream &operator<<(ostream &out, vector<A> &a) {
  out << "\n[";
  for (int(i) = (int)(0); (i) < (int)((int)a.size()); ++(i)) {
    if (i) out << ", ";
    out << a[i];
  }
  out << "]\n\n";
  return out;
}
void solution() {
  int a, b, c;
  cin >> a >> b >> c;
  int ans = 0;
  for (int(i) = (int)(0); (i) < (int)(100000000); ++(i)) {
    ans++;
    a *= 10;
    if (a / b == c) {
      cout << ans;
      return;
    }
    a %= b;
  }
  cout << -1;
}
int main() {
  ios_base::sync_with_stdio(false);
  solution();
  return 0;
}
