CF452C.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.

Alex 喜欢表演魔术。他有一个需要一副包含 $n$ 张牌的牌组的魔术。他有 $m$ 副完全相同的牌组，每副牌组均包含 $n$ 张互不相同的牌，这些牌组已被混合在一起。当 Alex 想要表演该魔术时，他会随机从中抽取 $n$ 张牌来组成一副用于表演的牌组。这副牌组看起来像一副正常的牌组，但其中可能包含某些牌的重复。

该魔术的具体流程如下：首先，Alex 让你从这副牌组中随机选择一张牌；你记住这张牌后将其放回牌组；接着 Alex 将牌组洗匀，然后从中抽出一张牌。若抽出的牌与你之前记住的牌相同，则该魔术成功。

你认为 Alex 并非一位高明的魔术师，他只是从牌组中随机抽取一张牌。请在这一假设下，计算该魔术成功的概率。

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.

输入的第一行包含两个整数 $n$ 和 $m$（$1 ≤ n, m ≤ 1000$），以空格分隔——分别表示每副牌的卡片数量和牌副数量。

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.

在输出的唯一一行中，打印一个浮点数——Alex 成功完成该魔术的概率。你的答案的相对误差或绝对误差不应超过 $10^{-6}$。

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

在第一个样例中，以概率 ，Alex 将从两个不同的牌堆中各选一张点数相同的牌来表演该戏法。此时戏法必定成功。

在剩余的 概率下，他选取了两张点数不同的牌，此时成功完成该戏法的概率为 。

最终的概率为