# Happy day?

# Happy day?

*На уроке биологии:*

— *К какому царству принадлежит мышь?*

— *К мышиному*!

Из школьной жизни

Murchik is the cat who likes to hunt. This hobby is so important for him that he thinks the day is happy if he had a successful hunt that day. Murchik hunts every day and usually on mice.

Going out to hunt, Murchik knows that there are only **n** mice. In addition, an experienced cat knows for each mouse the probability to catch it. Murchik believes that a day for him is happy if he catches at least **k** mice.

Since Murchik has big problems with mathematics, like his friend Murzik, he asks you to help him to calculate the probability that a day will be happy for him.

#### Input

The first line contains two integers: the amount of mice **n** (**0** < **n** < **21**), on which Murchik will hunt and the minimum number of mice **k** (**0** ≤ **k** ≤ **n**) that Murchik must to catch so that the day will be happy for him.

Next **n** lines contains **n** real numbers `p`

- the probability that Murchik can catch the _{i}**i**-th mice.

#### Output

Print the probability that the day will be happy for Murchik. Print the probability with **8** decimal digits.

3 1 0.5 0.5 0.5

0.8750000000

3 2 0.5 0.5 0.5

0.5000000000

3 3 0.5 0.5 0.5

0.12500000