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:

from collections import Counter,defaultdict,deque
#from heapq import *
#from itertools import *
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#dirs = [[1,0],[0,1],[-1,0],[0,-1]]
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
#from math import *

import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
#MOD = 10**9+7
def solve():
    a,b,c,d = [int(x) for x in input().split()]
    p1 = a/b
    p2 = c/d
    p = p1/(1-(1-p1)*(1-p2))
    print(p)

tt = 1#int(input())
for test in range(tt):
    solve()

 


 
 
 
 
 
 
 
 
 
 
 
 
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