Partition Number

You are given an integer set $A=\\{a\_1,a\_2,\ldots,a\_n\\}$. Please calculate the number of solutions for equation $x\_1+x\_2+\ldots+x\_k=m$, where $x\_i$ are positive integers, $x\_1 \le x\_2 \le \ldots \le x\_k$ and $x\_i \not \in A$.

As the answer may be very large, you are only asked to calculate it modulo $(10^9 + 7)$.

There are multiple test cases. The first line of the input contains an integer $T$ indicating the number of test cases. For each test case:

The first line contains two integers $n$ and $m$ ($1 \le n \le 500$, $n \le m \le 3 \cdot 10^5$).

The second line contains $n$ integers $a\_1,a\_2,\ldots,a\_n$ ($1 \le a\_i \le m$, $a\_i \ne a\_j$ for all $i \ne j$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $500$.

For each test cases, output an integer denoting the answer.

There are $5$ solutions for $m=4$ if the constraints set $A$ is empty. They are: $\begin{aligned} 4 & = & 1+1+1+1 \\\ {} & = & 1+1+2 \\\ {} & = & 1+3 \\\ {} & = & 2+2 \\\ {} & = & 4 \end{aligned}$