Wedding Invitation#1264
Spring was in the air, and everything seemed calm until Vasya and Natalia suddenly decided to get married. After dating for a long time, they finally chose to take the plunge.
They did not want to delay, so they set the date for October 2nd. Almost everything was ready; the only task left was inviting guests to the celebration. This turned out to be quite a challenge. Some guests would attend, while others might not, and Vasya and Natalia were eager to know approximately how many would actually show up. To get a better idea, they decided to survey the invitees about their attendance. Although everyone responded with a "YES", not all of them truly meant it. Therefore, Natalia and Vasya needed a way to calculate the exact number of guests who would definitely attend. Each invitee has a reliability factor, x_i, representing the probability that they will keep their word. Using this information, you need to determine the probability that exactly guests will attend the wedding.
The first line contains the number of test cases, . Each test case is described in the following lines. The first line of each test case contains two integers, and , where is the number of invitees (0 \leq N \leq 100, 0 \leq K \leq N). The next lines of each test case provide the probabilities x_i (0 \leq x_i \leq 1).
For each test case, output the required probability with decimal places on a separate line.
Example 1