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 PYTHON3):

Solution:
import itertools
import math


S = 1000000


if __name__ == '__main__':
    fact = list(itertools.accumulate(range(S + 1), lambda x, y: x + math.log(y)))
    n, m = [int(x) for x in input().split()]
    res = 0.0
    for i in range(1, min(n, m) + 1):
        res += math.exp(
                math.log(n) + (fact[m] - fact[i] - fact[m - i]) +\
                        (fact[(n - 1) * m] - fact[n - i] - fact[(n - 1) * m - n + i]) -\
                        (fact[n * m] - fact[n] - fact[n * m - n]) +\
                        math.log((1.0 * i / n) ** 2))
    print(res)