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;
void positionInFraction();
int main() {
  positionInFraction();
  return 0;
}
void positionInFraction() {
  int b, c, rpta, division;
  long long a, posicion;
  cin >> a >> b >> c;
  bool hayRpta = false;
  posicion = 1;
  while (posicion < 100000 and !hayRpta) {
    a = a * 10;
    division = a / b;
    if (division % 10 == c) {
      cout << posicion;
      hayRpta = true;
      break;
    }
    a = a % b;
    posicion++;
  }
  if (hayRpta) {
  } else {
    cout << -1;
  }
}
