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>
int main(int argc, char const *argv[]) {
  int a, b, c;
  while (scanf("%d%d%d", &a, &b, &c) != EOF) {
    int mod = a % b * 10;
    int counter = 1;
    while (counter < b + 1) {
      if (mod / b == c) {
        printf("%d\n", counter);
        break;
      }
      counter++;
      mod = mod % b * 10;
      if (counter == b + 1) {
        printf("-1\n");
      }
    }
  }
  return 0;
}
