Games

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Alice and Bob are playing a stone game. There are $n$ piles of stones. In each turn, a player can remove some stones from a pile (the number must be positive and not greater than the number of remaining stones in the pile). One player wins if he or she remove the last stone and all piles are empty. Alice plays first.
To make this game even more interesting, they add a new rule: Bob can choose some piles and remove entire of them before the game starts. The number of removed piles is a nonnegative integer, and not greater than a given number $d$. Note $d$ can be greater than $n$, and in that case you can remove all of the piles.
Let $ans$ denote the different ways of removing piles such that Bob are able to win the game if both of the players play optimally. Bob wants you to calculate the remainder of $ans$ divided by $10^9+7$.

Input

The first line contains an integer $T$, representing the number of test cases.
For each test cases, the first line are two integers $n$ and $d$, which are described above.
The second line are $n$ positive integers $a_i$, representing the number of stones in each pile.
$T \leq 5, n \leq 10^3, d \leq 10, a_i \leq 10^3$

Output

For each test case, output one integer (modulo $10^9 + 7$) in a single line, representing the number of different ways of removing piles that Bob can ensure his victory.

Sample Input

2
5 2
1 1 2 3 4
6 3
1 2 4 7 1 2 

Sample Output

2
5

Hint

Source

“浪潮杯”山东省第九届ACM大学生程序设计竞赛(感谢山东财经大学)