Happy day?#3531
At a biology lesson:
— What kingdom does a mouse belong to?
— To the mouse kingdom!
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 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 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.
The first line contains two integers: the number of mice (0 < n < 21), on which Murchik will hunt and the minimum number of mice (0 \leq k \leq n) that Murchik must catch so that the day will be happy for him.
The next lines each contain one real number p_i – the probability that Murchik can catch the -th mouse.
Print the probability that the day will be happy for Murchik. Print the probability with decimal digits.
Example 1
Example 2
Example 3