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 PYTHON):

Solution:
import sys
 
def main( ):
    str =    raw_input() 
    arr = str.split(' ')
    a = float( arr[0] )
    b = float( arr[1] )
    c = float( arr[2] )
    d = float( arr[3] )
    not_a =( a/b)
    not_a= 1-not_a
    not_b = (c/d)
    not_b= 1-not_b
    print a/( b* (1-not_a*not_b) )
 
main( )