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[100001], b[100001];
int main() {
  int n, n2, a, b, c;
  cin >> a >> b >> c;
  int h = 100001, k = b;
  int g = a % b;
  int c1 = 1;
  while (h) {
    int y = g * 10;
    int d = y / b;
    g = y % b;
    if (d == c) {
      cout << c1;
      return 0;
    }
    c1++;
    h--;
  }
  cout << "-1";
}
