Problem: Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.

The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.

You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.

Input

First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.

Output

On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.

Examples

Input

2 2


Output

0.6666666666666666


Input

4 4


Output

0.4000000000000000


Input

1 2


Output

1.0000000000000000

Note

In the first sample, with probability <image> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.

With the remaining <image> probability he took two different cards, and the probability of pulling off the trick is <image>.

The resulting probability is <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
class C_ {};
template <typename T>
C_& operator<<(C_& __m, const T& __s) {
  if (!1) cerr << "\E[91m" << __s << "\E[0m";
  return __m;
}
C_ merr;
struct __s {
  __s() {
    if (1) {
      ios_base::Init i;
      cin.sync_with_stdio(0);
      cin.tie(0);
    }
  }
  ~__s() {
    merr << "Execution time: " << fixed << setprecision(3)
         << (double)clock() / CLOCKS_PER_SEC << " s.\n";
  }
} __S;
int main(void) {
  int n, m;
  long double sum = 0;
  cin >> n >> m;
  for (int i = 1; i <= min(m, n); i++) {
    long double mm = 1;
    for (int j = 1; j <= i; j++) {
      mm *= (n - i + j) * 1.0L * (m - i + j) / (1.0L * j);
    }
    for (int j = 1; j <= n; j++) {
      if (j <= n - i) mm *= (m * n * 1.0L - m - (n - i) + j * 1.0L);
      mm /= (m * 1.0L * n - n + j);
    }
    mm *= (i * 1.0L * i) / (n * 1.0L * n);
    sum += mm;
  }
  sum *= n;
  cout << fixed << setprecision(10) << sum << '\n';
  return 0;
}