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::sync_with_stdio(false);
  int a, b, c, i = -1, pos[505] = {0};
  cin >> a >> b >> c;
  if (a > b) {
    a = a % b;
  }
  while (i < 500) {
    a = a * 10;
    while (a < b) {
      i++;
      pos[i] = 0;
      a = a * 10;
    }
    i++;
    pos[i] = a / b;
    a = a % b;
    if (a == 0) {
      break;
    }
  }
  bool flag = false;
  for (i = 0; i < 500; i++) {
    if (pos[i] == c) {
      flag = true;
      break;
    }
  }
  if (flag) {
    cout << i + 1 << "\n";
  } else {
    cout << "-1\n";
  }
  return 0;
}
