F. Expected Mediantime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputArul has a binary array$$$^{\text{∗}}$$$ $$$a$$$ of length $$$n$$$.He will take all subsequences$$$^{\text{†}}$$$ of length $$$k$$$ ($$$k$$$ is odd) of this array and find their median.$$$^{\text{‡}}$$$What is the sum of all these values?As this sum can be very large, output it modulo $$$10^9 + 7$$$. In other words, print the remainder of this sum when divided by $$$10^9 + 7$$$.$$$^{\text{∗}}$$$A binary array is an array consisting only of zeros and ones.$$$^{\text{†}}$$$An array $$$b$$$ is a subsequence of an array $$$a$$$ if $$$b$$$ can be obtained from $$$a$$$ by the deletion of several (possibly, zero or all) elements. Subsequences don't have to be contiguous.$$$^{\text{‡}}$$$The median of an array of odd length $$$k$$$ is the $$$\frac{k+1}{2}$$$-th element when sorted.InputThe first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq k \leq n \leq 2 \cdot 10^5$$$, $$$k$$$ is odd) — the length of the array and the length of the subsequence, respectively.The second line of each test case contains $$$n$$$ integers $$$a_i$$$ ($$$0 \leq a_i \leq 1$$$) — the elements of the array.It is guaranteed that sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.OutputFor each test case, print the sum modulo $$$10^9 + 7$$$.ExampleInput84 31 0 0 15 11 1 1 1 15 50 1 0 1 06 31 0 1 0 1 14 31 0 1 15 31 0 1 1 02 10 034 171 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1Output2
5
0
16
4
7
0
333606206
NoteIn the first test case, there are four subsequences of $$$[1,0,0,1]$$$ with length $$$k=3$$$: $$$[1,0,0]$$$: median $$$= 0$$$. $$$[1,0,1]$$$: median $$$= 1$$$. $$$[1,0,1]$$$: median $$$= 1$$$. $$$[0,0,1]$$$: median $$$= 0$$$. The sum of the results is $$$0+1+1+0=2$$$.In the second test case, all subsequences of length $$$1$$$ have median $$$1$$$, so the answer is $$$5$$$.