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:
from  decimal import *

def C(n,m):
    if m>n : return 0
    if m==0 or m==n : return 1
    if m>n-m : m=n-m
    ret = 1
    i,j = n,1
    while j<=m :
        ret = ret*i/j
        i=i-1
        j=j+1
    return ret

n,m = map(int,raw_input().split())
ans = C(m,1)*C(n*m-1,n-1)
if n>1 : ans += 2*C(m,2)*C(n*m-2,n-2)
ans = Decimal(1.0/n) * Decimal(ans) / Decimal(C(n*m,n))
print '%.16f' %ans