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 a, b, c;
int main() {
  cin >> a >> b >> c;
  int cnt = 0;
  a *= 10;
  while (cnt <= 1000000) {
    long long d = a / b;
    long long rem = d * b;
    rem = a - rem;
    rem *= 10LL;
    a = rem;
    if (d == c) break;
    cnt++;
  }
  if (cnt == 1000001) {
    cout << -1 << endl;
  } else
    cout << cnt + 1 << endl;
}
