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:
import sys
import math
from decimal import *

def nchoosek(n, k):
    if k == 0:
        return 1
    if n == 0:
        return 0
    if n <= 1000:
        return math.factorial(n) / math.factorial(k) / math.factorial(n-k)
    else:
        ans = 1
        ncopy = n
        for i in range(k):
            ans *= ncopy
            ncopy -= 1
        ans /= math.factorial(k)
        return ans

n, m = [int(x) for x in raw_input().strip().split()]

ans = 0

tot = Decimal(nchoosek(m*n-1, n-1))
for i in range(0, min(m, n)):
    p = Decimal(nchoosek(m*(n-1), (n-1)-i) * nchoosek(m-1, i))/tot
    if p < 0.0000000001:
        break
    ans += p*(Decimal(i+1)/Decimal(n))

print ans