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:
#!/usr/bin/python
a, b, c, d = map(float, raw_input().split())
p1, p2, r = 1, 1, 0
for _ in xrange(10000):
    r+=a/b*p1*p2
    p1*=(b-a)/b
    p2*=(d-c)/d
print r