ZCR - Zen And His Crush


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

hide comments
mahilewets: 2017-09-02 16:26:41

The solution immediately comes to mind after reading the statement.

wisfaq: 2017-03-28 09:58:36

@anand25021998: I shouldn't know what is so special about k=0.

anand25021998: 2017-03-27 17:28:32

The testcases are weak I guess. I submitted 2 solns and both were accepted but in only one of them I took care of k=0.Hope u take notice of this


Added by:e_coder
Date:2017-03-27
Time limit:0.5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All