A16400 | Construct Tree

You are given an array of integers $l_1, l_2, \dots, l_n$ and an integer $d$ . Is it possible to construct a tree satisfying the following three conditions?

- The tree contains $n + 1$ nodes.
- The length of the $i$ -th edge is equal to $l_i$ .
- The (weighted) diameter of the tree is equal to $d$ .

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 250$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ , $d$ ( $2 \leq n \leq 2000, 1 \leq d \leq 2000$ ).

The second line of each test case contains $n$ integers $l_1, l_2, \dots, l_n$ ( $1 \leq l_i \leq d$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$ .

For each test case, output $\texttt{Yes}$ if it is possible to construct a tree that satisfies all the conditions, and $\texttt{No}$ otherwise.

You can print the letters in any case (upper or lower).