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:
from Queue import * # Queue, LifoQueue, PriorityQueue
from bisect import * #bisect, insort
from datetime import * 
from collections import * #deque, Counter,OrderedDict,defaultdict
import calendar
import heapq
import math
import copy
import itertools

def solver():
    a,b,c,d = map(float,raw_input().split())

    r = ((b-a)/b) * ((d-c)/d)

    print (a/b) * ((1-(r**10000))/(1-r))


if __name__ == "__main__":
    solver()