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 math
import decimal
import functools


@functools.lru_cache(maxsize=None)
def factorial(n):
    return math.factorial(n)


@functools.lru_cache(maxsize=None)
def binomial(k, n):
    if k > n // 2:
        return product(range(k + 1, n + 1)) / factorial(n - k)
    else:
        return product(range(n - k + 1, n + 1)) / factorial(k)


def P(k, n, m):
    return k ** 2 / n * binomial(k, n) * product((m - i) / (m * n - i) for i in range(k)) * product(
        (m * n - i - (m - k)) / (m * n - i) for i in range(k, n))


def product(iterable):
    res = 1
    for e in iterable:
        res *= e
    return res


def solve(n, m):
    return sum(P(k, n, m) for k in range(1, min(n, m) + 1))


if __name__ == '__main__':
    n, m = map(int, input().split())
    print(solve(n, m))