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:
def c(x,n,k):
    if k<0 or k>n:
        return 0
    elif k>n/2:
        return c(x,n,n-k)
    else:
        for i in range(k):
            x*=n-i
            x/=i+1
        return x
def rvc(x,n,k):
    if k>n/2:
        return rvc(x,n,n-k)
    else:
        for i in range(k):
            x/=n-i
            x*=i+1
        return x
n,m=map(int,raw_input().split())
ans=0.0
for i in range(m):
    a=n-1-i
    b=(n-1)*m
    x=i
    y=m-1
    t=float(i+1)/n
    if t>1:
        t=0
    else:
        for j in range(a):
            t*=b-j
            t/=b+y-j
        for j in range(x):
            t*=y-j
            t/=j+1
            t*=a+1+j
            t/=b+y-a-j
    ans+=t
print ans