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
a, b, c, d = map(int, input().split())
s = a/b
z = c/d
psw = 0
c = 0
while True:
    temp = ((1-s)**c)*((1-z)**c)*s
    psw += temp
    c += 1
    if temp < 10**(-11):
        break
print(round(psw, 7))