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() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int a, b, c;
  cin >> a >> b >> c;
  long double k = a / b;
  long double k1 = k;
  int count = 0;
  int s = 0;
  long long int temp = k1 - int(k), temp1 = -1;
  bool flag = 1;
  int i = 1;
  while (flag) {
    temp1 = (a * 10) / b;
    a = (a * 10) % b;
    if (c == temp1) {
      flag = 0;
      break;
    }
    i++;
    if (i >= 100000) break;
  }
  if (!flag)
    cout << i;
  else
    cout << -1;
}
