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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int a, b;
  int c;
  while (cin >> a >> b >> c) {
    int cnt = 1;
    a %= b;
    a *= 10;
    bool val = false;
    set<int> s;
    s.insert(a);
    for (int i = 0; i < 100000000; i++) {
      if (a / b == c) {
        val = true;
        break;
      }
      a %= b;
      a *= 10;
      if (s.find(a) != s.end()) break;
      s.insert(a);
      cnt++;
    }
    if (val)
      cout << cnt << "\n";
    else
      cout << -1 << "\n";
  }
  return 0;
}
