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 math
import re
from fractions import Fraction
from collections import Counter

class Task:
    a, b, c, d = 0, 0, 0, 0
    answer = 0
    
    def __init__(self):
        self.a, self.b, self.c, self.d = [int(x) for x in input().split()]

    def solve(self):
        a, b, c, d = self.a, self.b, self.c, self.d
        p = a / b
        q = c / d
        x = (1 - p) * (1 - q)
        self.answer = p / (1 - x)

    def printAnswer(self):
        print(self.answer)

task = Task()
task.solve()
task.printAnswer()