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() {
  int a, b, c, cnt = 1;
  cin >> a >> b >> c;
  if (a % b == 0) {
    if (c == 0)
      cout << 1 << '\n';
    else
      cout << -1 << '\n';
    return 0;
  } else {
    int mod = a % b;
    if (a < b) a *= 10;
    while (cnt <= 100000) {
      mod = mod * 10;
      if (mod / b == c) {
        cout << cnt << '\n';
        return 0;
      }
      mod = mod % b;
      cnt++;
    }
  }
  cout << -1 << '\n';
}
