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;
long long a, b, c, d = -1, i = 0;
int main() {
  scanf("%d%d%d", &a, &b, &c);
  a = a % b;
  while (d != c) {
    d = a * 10 / b;
    a = a * 10 % b;
    i++;
    if (i > 1000000) break;
  }
  if (i <= 100005)
    printf("%d", i);
  else
    printf("-1");
}
