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 kt[1000000];
int x, y = 0;
long long a, b, c;
int main() {
  cin >> a >> b >> c;
  a = a % b;
  a *= 10;
  memset(kt, false, sizeof(kt));
  while (kt[a] == false) {
    y++;
    kt[a] = true;
    x = a / b;
    if (x == c) {
      cout << y;
      return 0;
    }
    a = (a % b) * 10;
  }
  cout << -1;
  return 0;
}
