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 long Q = 1e7;
const long long INF = 1e9;
const long long N = 1e5 + 3;
const long long mod = 1e9 + 7;
const long double eps = 1E-7;
long long n, x, k, m, cnt, a, b, r, t, R, d, f, c;
map<int, int> mp;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> a >> b >> c;
  a %= b;
  for (int i = 1; i <= 100000; i++) {
    a *= 10;
    t = a / b;
    a -= (a / b) * b;
    if (t == c) {
      cout << i;
      return 0;
    }
  }
  cout << -1;
}
