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;
const long long N = 3e5 + 7;
void solve() {
  long long a, b, c;
  cin >> a >> b >> c;
  for (long long i = 0; i < N; i++) {
    long long x = a * 10;
    long long r = x % b;
    long long q = x / b;
    if (q == c) {
      cout << i + 1;
      return;
    }
    a = r;
  }
  cout << -1;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  clock_t beg = clock();
  long long t = 1;
  while (t--) {
    solve();
  }
  cerr << "\nExecution time: " << (clock() - beg) / 1000 << '\n';
}
