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;
long long n, m, k;
int main() {
  cin >> n >> m >> k;
  for (int i = 0; i < 500000; i++) {
    n *= 10;
    long long c = n / m;
    n = n % m;
    if (c == k) {
      cout << i + 1 << endl;
      return 0;
    }
  }
  cout << -1 << endl;
}
