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 PYTHON):

Solution:
#sum(c = 0 to n) (Binomial[m*(n-1), n - c] * Binomial[m, c] * (c/n)^2)/Binomial[m*n, n]
from math import *
n, m = map(int, raw_input().split(" "))

d = {}
def b(n, k):
    #print n, k
    #raw_input("")
    if k > n or k < 0:
        return 0
    if (n, k) in d:
        return d[(n, k)]
    result = 0
    for i in range(1, k+1):
        result += log(n-i+1) - log(i)
    d[(n, k)] = result
    return result

print n*sum([exp(b((n-1)*(m), n - c) + b(m, c) - b(m*n, n)) * (c/float(n))**2 for c in xrange(1, min(n, m) + 1)])