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:
__author__ = 'liuchang'
import sys
a ,b , c ,d = map(int ,sys.stdin.readline().split(' '))

print 1.0 / ( 1 - ((d - c  + 0.0 ) / d) * (( b - a + 0.0 ) / b)) * ( ( a + 0.0)  / b)