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:
#!/usr/bin/python2
# -*- coding: utf-8 -*-

import sys
import os
from math import factorial

def main():
    n, m = map(int, sys.stdin.readline().split())
    ret = 0
    qq = n
    pp = 1
    for j in xrange(m*n - m + 1, m*n + 1):
        qq *= j
    for j in xrange(m*n - n - m + 1 + 1, m*n - n + 1):
        pp *= j
    for i in xrange(1, min(m, n) + 1):
        qq *= i
        q = qq
        pp *= (n - i + 1) * (m - i + 1)
        p = (10 ** 10) * i * i * pp
        #for j in xrange(n - i + 1, n + 1):
        #    p *= j
        #for j in xrange(m - i + 1, m + 1):
        #    p *= j
        #for j in xrange(m*n - n - m + i + 1, m*n - n + 1):
        #    p *= j
        qq *= (m*n - n - m + i + 1)
        ret +=  p / q

    print "%.9f" % (1e-10 * ret,)


if __name__ == '__main__':
    main()