Problem: SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is <image> for SmallR while <image> for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

Input

A single line contains four integers <image>.

Output

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

1 2 1 2


Output

0.666666666667

Solution (in PYTHON3):

Solution:
tmp = input().split(' ')
a = []
for i in range( 0 , 4 ):
    a.append( int( tmp[ i ] ) )

p1 = a[ 0 ] / a[ 1 ]
p2 = a[ 2 ] / a[ 3 ]

tot = 10 ** 5
ans = 0.0000000000000
for i in range( 0 , tot ):
    ans = ans + ( 1 - p1 ) ** i * ( 1 - p2 ) ** i * p1

print ( ans )