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(false);
  long long a, b, X;
  int c;
  cin >> a >> b >> c;
  bool M[b];
  long long ans = 1;
  a = a % b;
  M[a] = true;
  memset(M, false, sizeof(M));
  while (1) {
    X = (a * 10) / b;
    a = (a * 10) % b;
    if ((X) % 10 == c) {
      cout << ans;
      return 0;
    }
    if (M[a]) {
      cout << -1;
      return 0;
    } else
      M[a] = true;
    ans++;
  }
}
