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 MXX = 1e5 + 1;
const int MXN = 1e6 + 7;
bool used[MXX];
bool cmp(pair<int, pair<int, int> > a, pair<int, pair<int, int> > b) {
  if (a.first == b.first) {
    if (a.second.first == b.second.first) {
      return (a.second.second < b.second.second);
    }
    return (a.second.first < b.second.first);
  }
  return (a.first < b.first);
}
int a, b, c;
string s;
string tostring(int x) {
  string res = "";
  while (x) {
    res += (x % 10) + '0';
    x /= 10;
  }
  reverse(res.begin(), res.end());
  return res;
}
int main() {
  cin >> a >> b >> c;
  for (int i = 1; i <= 1e7; i++) {
    a *= 10;
    if (a / b == c) return cout << i, 0;
    a %= b;
  }
  cout << -1;
  return 0;
}
