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:
F=[1,1]
for i in range(2,1001):
    F.append(F[-1]*i)
def ncr(x,y):
    return F[x]//(F[y]*F[x-y])

n,m=map(int,input().split())
P=[0]*2000

for j in range(1,min(m,n)+1):
    mine=m
    total=n*m
    p=1
    for x in range(j):
        p*=mine/total
        mine-=1
        total-=1
    for x in range(n-j):
        p*=(total-mine)/total
        total-=1
    p*=n
    p*=ncr(n,j)
    P[j]=p

ans=0

for j in range(1,min(m,n)+1):
    # What is the probability that the deck will contain j cards of type i
    p=P[j]
    ans+=P[j]*(j*j)/(n*n)
print(ans)