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 main() {
  long long a, b, c, pos = 0, p1, p2;
  cin >> a >> b >> c;
  map<long long, long long> mp;
  p1 = a % b;
  pos = 1;
  while (1) {
    if (mp[p1]) {
      break;
    }
    mp[p1] = 1;
    p1 *= 10;
    p2 = p1 / b;
    if (p2 == c) {
      cout << pos;
      return 0;
    }
    p1 = p1 % b;
    pos++;
  }
  cout << "-1";
  return 0;
}
