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 double PI = 3.14159265;
const long long int MAX = 1000000;
int d[MAX] = {0};
int main() {
  ios::sync_with_stdio(false);
  int a, b, c, t = 0;
  cin >> a >> b >> c;
  vector<int> ans;
  while (true) {
    int temp = 0;
    while (true) {
      a = a * 10;
      temp++;
      if (temp > 1) {
        ans.push_back(0);
        t++;
      }
      if (a >= b) break;
    }
    if (d[a % b] != 0) {
      break;
    }
    d[a % b]++;
    ans.push_back(a / b);
    t++;
    if (a % b == 0) {
      ans.push_back(0);
      t++;
      break;
    }
    if (a / b == c) {
      break;
    }
    a %= b;
  }
  for (int i = 0; i < t; i++) {
    if (ans[i] == c) {
      cout << i + 1 << endl;
      return 0;
    }
  }
  cout << -1 << endl;
  return 0;
}
