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:
epsilon=0.000000001
[a,b,c,d]=[float(i) for i in raw_input().split()]
j=0
p=(a/b)
q=((b-a)/b)*((d-c)/d)
r=((b-a)/b)*(c/d)
t=((b-a)/b)*((d-c)/d)
##p1=r
##p2=p1+t*r
##i=2
##while p2-p1<epsilon:
##    p1=p2
##    p2=p1+(t**i)*r
##    i+=1
##print 1.0-p2
p1=p
p2=p1+q*p
i=2
while p2-p1>epsilon:
    p1=p2
    p2=p2+(q**i)*p
    i+=1
print p2
##n=int(raw_input())
##for i in range(n):
##    j=raw_input()
##    ##print j[-1:-5:-1]
##    if (j[-1:-6:-1]==".alal" and j[0:5]!="miao."):
##        print "Freda's"
##    elif (j[0:5]=="miao." and j[-1:-6:-1]!=".alal" ):
##        print "Rainbow's"
##    else:
##        print "OMG>.< I don't know!"
##
##