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 gcd(int a, int b) {
  int c;
  while (b) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
int main() {
  int a, b, c, d, e, i;
  cin >> a >> b >> c;
  d = gcd(a, b);
  a /= d;
  b /= d;
  d = a / b;
  a -= d * b;
  a *= 10;
  for (i = 1; i <= 100000; i++) {
    d = a / b;
    a -= d * b;
    if (d == c) break;
    a *= 10;
  }
  if (i > 100000)
    cout << "-1" << endl;
  else
    cout << i << endl;
  return 0;
}
