A9474 | Magic Trick

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.

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.

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 $10^{-6}$ .