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 numr, denr, c;
void fractionToDecimal(int numr, int denr) {
  string res;
  map<int, int> mp;
  mp.clear();
  int rem = numr % denr;
  int ans = 0;
  while ((rem != 0) && (mp.find(rem) == mp.end())) {
    mp[rem] = res.length();
    rem = rem * 10;
    int res_part = rem / denr;
    if (res_part == c) {
      cout << ans + 1 << endl;
      exit(0);
    }
    rem = rem % denr;
    ans++;
  }
  if (rem == 0 && c == 0)
    cout << ans + 1 << endl;
  else
    cout << -1 << endl;
}
int main() {
  cin >> numr >> denr >> c;
  fractionToDecimal(numr, denr);
  return 0;
}
