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:
def main():
   s = raw_input()
   prs = s.split()
   for i in range(0, len(prs)):
       prs[i] = (float)(prs[i])
   p = prs[0]/prs[1]
   q = prs[2]/prs[3]
   res = p/(1-(1-p)*(1-q))
   print(res)

if __name__ == '__main__':
    main()