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 math as mt
import bisect
#input=sys.stdin.buffer.readline  
#t=int(input())
t=1
for __ in range(t):
    #s=input()
    #n=int(input())
    a,b,c,d=map(int,input().split())
    #l=list(map(int,input().split()))
    r=(1-(a/b))*(1-(c/d))
    ans=(a/b)/(1-r)
    print(ans)