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;
const int SZ = 104;
const double EPS = 1e-7;
int a, b, c;
void read() { cin >> a >> b >> c; }
void solve() {
  a -= a / b * b;
  for (int i = 0; i < 1e5; ++i) {
    a *= 10;
    if (c == a / b) {
      cout << i + 1;
      return;
    }
    a -= a / b * b;
  }
  cout << -1;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  read();
  solve();
  return 0;
}
