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 a, b, c, l = 1, i, p = 1, oa, r;
  scanf("%d%d%d", &a, &b, &c);
  while (1) {
    for (oa = a, i = 0; i < l; i++, p++) {
      r = 10 * a / b;
      if (r == c) break;
      a = 10 * a - r * b;
      if (a == oa) break;
    }
    if (r == c) {
      printf("%d\n", p);
      break;
    } else if (a == oa) {
      printf("-1\n");
      break;
    } else {
      oa = a;
      l *= 2;
    }
  }
  return 0;
}
