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 long long mul = 1e9 + 7;
const int maxn = 1e6 + 1;
long long a, b;
vector<long long> du, thuong;
int kt[maxn];
int c;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> b >> c;
  long long d = a % b;
  du.push_back(d);
  kt[a % b]++;
  while (kt[a % b] < 2) {
    a *= 10;
    du.push_back(a % b);
    thuong.push_back(a / b);
    kt[a % b]++;
    a = (a % b);
  }
  bool f = true;
  for (int i = 0; i < thuong.size(); i++) {
    if (c == thuong[i]) {
      cout << i + 1;
      f = false;
      break;
    }
  }
  if (f == true) cout << -1;
}
