If the length of a sequence $$$s$$$ is not less than $$$3$$$,we call $$$s$$$ a valid sequence.
For a valid sequence $$$s$$$,we define the extended average of $$$s$$$ as the average of the remaining numbers after removing one of the maximum value and one of the minimum value in $$$s$$$.
For example,$$$s=\{1,2,1,3,5,3\}$$$,the extended average of $$$s$$$ is $$$\frac{(1+2+3+3)}{4}=2.25$$$.
You're given a sequence $$$a$$$ of size $$$n$$$ and an integer $$$x$$$.Your task is to count the number of valid subsequence $$$b$$$ of $$$a$$$,that the extended average of $$$b$$$ is equal to $$$x$$$.
Since the answer may be very large,output it modulo $$$10^9+7$$$.
The first line of contains two integers $$$n,x(1 \leq n,x \leq 100)$$$.
The second line contains $$$n$$$ integers $$$a_1,a_2,...,a_n(1 \leq a_i \leq 100)$$$.
Output an integer — the number of valid subsequence $$$b$$$ of $$$a$$$,that the extended average of $$$b$$$ is equal to $$$x$$$(modulo $$$10^9+7$$$).
5 3 5 4 3 2 1
6
6 6 6 6 6 6 6 6
42
16 8 15 3 15 16 5 13 16 13 15 6 14 6 1 3 11 14
689
Test case $$$1$$$:
The following are all subsequences meet the conditions:
$$$\{a_1,a_2,a_3,a_4,a_5\}$$$,$$$\{a_1,a_2,a_4,a_5\}$$$,$$$\{a_1,a_3,a_4\}$$$,$$$\{a_1,a_3,a_5\}$$$,$$$\{a_2,a_3,a_4\}$$$,$$$\{a_2,a_3,a_5\}$$$.
Test case $$$2$$$:
All subsequence with a length of no less than $$$3$$$ meet the conditions.
