Magic Trick

1000ms

262144K

Description:

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.

Sample Input:

2 2

Sample Output:

0.6666666666666666

Sample Input:

4 4

Sample Output:

0.4000000000000000

Sample Input:

1 2

Sample Output:

1.0000000000000000

Note:

In the first sample, with probability $\text{[math]}$ 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 $\text{[math]}$ probability he took two different cards, and the probability of pulling off the trick is $\text{[math]}$ .

The resulting probability is $\text{[math]}$

Informação

Provedor Codeforces

Código CF452C