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 collections
import math

def readLine():
	return list(map(int, input().strip().split()))

def readInt():
	return int(input())

def readString():
	return input()

def tcase():
	t = readInt()
	for _ in range(t):
		solve()

def solve():
	n, m = readLine()

	f = [0] * (n*m+1)
	for i in range(2, n*m+1):
		f[i] = f[i-1] + math.log(i)

	def c(n, k):
		return f[n] - f[k] - f[n-k]


	ans = 0
	for num in range(1, min(n, m) + 1):
		temp = c(m, num) + c(m*(n-1), n-num) - c(m * n, n)
		pro = (num * num * 1.) / (n * 1.)
		# print(temp, pro)
		ans += pro * math.pow(math.e, temp)
	# ans = ans / math.comb(m * n, n)
	print(ans)

	


# tcase()
solve()