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;
bool comp(int num, int c) {
  if (num == c) return true;
  while (num != 0) {
    if (num & 10 == c) return true;
    num /= 10;
  }
  return false;
}
int main() {
  int a, b, c;
  scanf("%d %d %d", &a, &b, &c);
  set<int> res;
  int pos = 1;
  while (true) {
    if (res.count(a) > 0) {
      cout << -1 << endl;
      break;
    }
    res.insert(a);
    a *= 10;
    int val = a / b;
    if (comp(val, c)) {
      cout << pos << endl;
      break;
    }
    a %= b;
    pos++;
  }
}
