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 JC(int a, int b) {
  if (a % b == 0) return b;
  return JC(b, a % b);
}
int main() {
  int a, b, c, h;
  scanf("%d%d%d", &a, &b, &c);
  int k = JC(a, b);
  a /= k;
  b /= k;
  k = a / b;
  a = (a - k * b) * 10;
  for (int i = 1; i < 100001; i++) {
    h = a / b;
    a = (a - h * b) * 10;
    if (h == c) {
      printf("%d", i);
      return 0;
    }
  }
  printf("-1");
  return 0;
}
