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;
const int mod = int(1e9) + 7;
const int maxn = int(1e5) + 100;
int main() {
  int a, b, c;
  while (~scanf("%d%d%d", &a, &b, &c)) {
    bool flag = false;
    for (int i = 1; i < b + 1; i++) {
      a = a * 10;
      if (a / b == c) {
        printf("%d\n", i);
        flag = true;
        break;
      }
      a %= b;
    }
    if (!flag) printf("-1\n");
  }
}
