Partition Number

You are given an integer set $A=\{a_1,a_2,\ldots,a_n\}$. Calculate the number of solutions to the equation $x_1+x_2+\ldots+x_k=m$, where the $x_i$ are positive integers, $x_1 \le x_2 \le \ldots \le x_k$, and $x_i \not \in A$.

The answer can be very large, so calculate it modulo $(10^9 + 7)$.

The input contains multiple test cases. The first line holds an integer $T$, the number of test cases. Each test case is given as follows.

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 $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le m$, and $a_i \ne a_j$ for all $i \ne j$).

The sum of $n$ over all test cases does not exceed $500$.

For each test case, output one integer, the answer.

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