Magic Trick

题意翻译

有 $m$ 套相同的牌，每套牌有 $n$ 张互不相同的牌。将这 $m$ 套牌混合在一起后等概率随机地从中抽取 $n$ 张，并从抽出的 $n$ 张牌中等概率随机放回地抽取两张牌，求这两张牌相同的概率。 输出与答案误差不超过 $10^{-6}$ 即判为正确。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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} $ .

输入输出样例

输入样例 #1

2 2

输出样例 #1

0.6666666666666666

输入样例 #2

4 4

输出样例 #2

0.4000000000000000

输入样例 #3

1 2

输出样例 #3

1.0000000000000000

说明

In the first sample, with probability  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  probability he took two different cards, and the probability of pulling off the trick is . The resulting probability is