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 int maxn = 1e5 + 5;
const int mod = 1e9 + 7;
void solve() {
  long long a, b, c;
  cin >> a >> b >> c;
  map<long long, long long> mp;
  long long r = (a % b), ans = 1, tmp;
  while (!mp[r]) {
    mp[r] = 1;
    tmp = (r * 10) / b;
    if (tmp == c) {
      cout << ans << endl;
      return;
    }
    ans++;
    r = (r * 10) % b;
  }
  printf("-1\n");
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  while (t--) solve();
  return 0;
}
