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 main() {
  int res, a, b, c, d, aa;
  scanf("%d%d%d", &a, &b, &c);
  a = a % b;
  res = 0;
  int tmp = 0;
  while (true) {
    ++tmp;
    if (tmp > b) {
      res = -1;
      break;
    }
    if (a == 0) {
      if (c != 0) {
        res = -1;
      } else
        ++res;
      break;
    }
    int cnt = 0;
    while (a < b) {
      ++res;
      ++cnt;
      a *= 10;
    };
    if (cnt > 1 && c == 0) {
      res -= cnt - 1;
      break;
    }
    d = a / b;
    if (d == c) break;
    a = a % b;
  }
  printf("%d\n", res);
}
