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:
#!/bin/env python2
from decimal import Decimal
import sys

line = sys.stdin.readline().split()
a = int(line[0])
b = int(line[1])
c = int(line[2])
d = int(line[3])

A = Decimal(a) / Decimal(b)
B = Decimal(c) / Decimal(d)

Q = (Decimal(1) - A) * (Decimal(1) - B)

print A / (Decimal(1) - Q)