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, x;
  scanf("%d %d %d", &a, &b, &x);
  if (a != 0 && a >= b) {
    a = a - (a / b) * b;
  }
  a *= 10;
  int cont = 0;
  vector<int> v;
  while (cont <= b && a != 0) {
    if (a < b) {
      v.push_back(0);
    } else {
      v.push_back(a / b);
      a = a - (a / b) * b;
    }
    a *= 10;
    cont++;
  }
  if (a == 0) v.push_back(0);
  if (find(v.begin(), v.end(), x) != v.end()) {
    printf("%d\n", (find(v.begin(), v.end(), x) - v.begin()) + 1);
  } else
    puts("-1");
}
