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 ith coin is Pi. 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, Pi.

Output

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

Example

Input:
1
3 2
0.0 0.5 1.0
Output:
0.5000000000