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 pi - the probability that Murchik can catch the i-th mice.

Output

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