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;
template <class T>
int size(const T &x) {
  return x.size();
}
template <class T>
T mod(T a, T b) {
  return (b + (a % b)) % b;
}
const int INF = ~(1 << 31);
const double EPS = 1e-9;
const double PI = acos(-1);
int main() {
  int a, b, c, cont = 1;
  cin >> a >> b >> c;
  vector<int> seen(1e5);
  a %= b;
  while (true) {
    if (seen[a]) break;
    seen[a] = true;
    a *= 10;
    if (a / b == c) {
      cout << cont << '\n';
      return 0;
    }
    a %= b;
    cont++;
  }
  cout << -1 << '\n';
  return 0;
}
