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 Count(int a) {
  int l = 0;
  if (a / 10 == 0) {
    return 1;
  }
  while (a / 10) {
    l += 1;
    a /= 10;
  }
  return l;
}
int main() {
  int n = 0, a = 0, b = 0, c = 0, p = -1;
  cin >> a >> b >> c;
  int ans = 1;
  int bl = Count(b);
  for (int i = 1; i <= 1e6; i++) {
    int u = Count(a);
    if (u + 1 <= bl) a *= 10;
    if (a < b && u == bl) a *= 10;
    int h = a / b;
    if (h == c) {
      p = i;
      break;
    }
    a -= b * h;
  }
  cout << p << endl;
  return 0;
}
