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;
template <typename T>
inline T read(T &x) {
  x = 0;
  int f = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    f |= (ch == '-'), ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) + ch - '0', ch = getchar();
  }
  return x = f ? -x : x;
}
int position_of_digit(int a, int b, int c) {
  a = a % b;
  for (int i = 1; i <= b; i++) {
    a *= 10;
    if (a / b == c) return i;
    a %= b;
  }
  return -1;
}
int main(void) {
  int a, b, c;
  read(a), read(b), read(c);
  int ans = position_of_digit(a, b, c);
  cout << ans << "\n";
  return 0;
}
