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;
struct _nl {
} nl;
bool _ns = 0;
template <typename T>
void _p(const T& _) {
  if constexpr (is_same<T, _nl>()) {
    cout << "\n";
    _ns = 0;
  } else {
    if (_ns) cout << " ";
    cout << _;
    _ns = 1;
  }
}
template <typename... T>
void out(const T&... _) {
  (_p(_), ...);
}
int ii() {
  int _;
  cin >> _;
  return _;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int cards_in_desk = ii();
  int ndesks = ii();
  if (cards_in_desk == 1 && ndesks == 1)
    out(1, nl);
  else {
    double ans = (1.0 + (cards_in_desk - 1) * (ndesks - 1) /
                            ((double)(cards_in_desk * ndesks) - 1)) /
                 cards_in_desk;
    cout << setprecision(12) << ans << endl;
  }
  return 0;
}