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 MAX = 1844674407370955161;
int main() {
  long long x, y, c;
  cin >> x >> y >> c;
  long long ind = -1, ctr = 1;
  long long rem = x;
  while (ctr < 100000) {
    rem = rem % y;
    rem *= 10;
    long long t = rem / y;
    if (t == c) {
      ind = ctr;
      break;
    }
    ctr++;
  }
  cout << ind << endl;
  return 0;
}
