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:
# MC621 - Desafios de Programacao II - 2s2020
# Problema G: Archer

# utiliza split para possibilitar a leitura das 3 variaveis
a, b, c, d = input().split()

# converte os valores das variaveis para int 
a, b, c, d = int(a), int(b), int(c), int(d)

# calculo da probabilidade
"""
- a formula fechada se da considerando as probabilidades e seus respectivos complementos
- nos levando a uma soma dos termos de uma PG infinita
  S = a/(1-r)
- sendo
  'a', a probabilidade de acerto a/b
  'r', o complemento de a/b vezes o complemento de c/d
"""
prob = a/b/(1-(1-a/b)*(1-c/d))

# impressao do resultado
print(round(prob, 12))