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 MAXN = 2 * 1e5 + 6;
const int maxn = 1e9 + 6;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  int n, m, k, cnt = 1;
  bool flag = false;
  scanf("%d%d%d", &n, &m, &k);
  while (cnt <= MAXN) {
    n *= 10;
    if (n / m == k) {
      flag = true;
      break;
    }
    n %= m;
    cnt++;
  }
  printf("%d\n", flag ? cnt : -1);
  return 0;
}
