Zen has a Crush and is always fantasizing about her. He is so restless now, that he has decided to meet her and express his immense feelings about her. He fears a lot of being rejected that's why he wants to examine his luck. Zen has N biased coins where the probability of getting Head from i^th coin is P_i. His luck of being accepted is the probability of getting exactly K heads when N coins are tossed simultaneously.

Zen is weak in programming and asking for help. Can you help him to calculate his luck?

Input

First Line of the input file contains, T-number of test cases. (1 <= T <= 100). Each test case followed by two integers, N and K. (1 <= N <= 1000, 0 <= K <= N) Next line contains N-space separated real values, P_i.

Output

For each test case, you have to print desired output (with up to 10 decimal places.)

Example

Input:
13 20.0 0.5 1.0
Output:
0.5000000000