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:
import sys
import bisect
from collections import Counter,defaultdict as dd
def data(): return sys.stdin.readline().strip()
def out(var): sys.stdout.write(str(var))
def l(): return list(sp())
def strl(): return list(strsp())
def sp(): return map(int, data().split())
def strsp(): return map(str, data().split())

a,b,c,d=sp()
p=(a/b)
q=(1-(a/b))*(1-(c/d))
print(p/(1-q))