Chocolate Wholesaler

A chocolate company is running a promotion: some chocolate bars hide a surprise inside, but you cannot tell from the outside whether a given bar contains one.

Fortunately, you can analyze each bar and determine the probability that it contains a surprise. Chocolates arrive at the wholesaler in cartons of $n$ bars, and you may only buy a whole carton, never a single bar.

Buying a carton pays off only if it contains at least $k$ surprises. Assuming the surprises occur independently across bars, compute the probability that a carton of $n$ chocolates contains at least $k$ surprises.

The first line contains the number of test cases $d$ $(1 \le d \le 100)$.

For each test case, the first line contains two integers $n$ and $k$ $(1 \le n \le 10000,\ 0 \le k \le n)$. The second line contains $n$ real numbers giving the probability that each chocolate contains a surprise; every probability is given to four decimal places.

For each test case, print on its own line the probability that a carton of $n$ chocolates contains at least $k$ surprises. Round the result to four decimal places.