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 const N = 2e5 + 5;
vector<int> v;
long long x, y, z, n, m;
long long a = 0, b = 0;
int main() {
  cin >> x >> y >> z;
  x = x % y;
  a = 1e6;
  while (a--) {
    x *= 10;
    n = x / y;
    b++;
    if (n == z) {
      cout << b << endl;
      return 0;
    }
    x -= (n * y);
  }
  cout << -1 << endl;
  return 0;
}
