CF1917F.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 $d$.

给你一个整数数组 $l_1, l_2, \dots, l_n$ 和一个整数 $d$。能否构造一棵满足以下三个条件的树？

• 该树包含 $n + 1$ 个节点；
• 第 $i$ 条边的长度等于 $l_i$；
• 该树的（带权）直径等于 $d$。

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 $2000$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 250$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $d$（$2 \leq n \leq 2000$，$1 \leq d \leq 2000$）。

每个测试用例的第二行包含 $n$ 个整数 $l_1, l_2, \dots, l_n$（$1 \leq l_i \leq d$）。

保证所有测试用例中 $n$ 的总和不超过 $2000$。

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).

对于每个测试用例，如果能够构造出一棵满足所有条件的树，则输出 $\texttt{Yes}$，否则输出 $\texttt{No}$。

字母大小写均可（大写或小写）。

Below, you are given the illustrations of trees for the first and third test cases. One of the diameters is highlighted by coloring its edges in red.

下面给出了第一个和第三个测试用例的树的示意图。其中一条直径通过将其边涂成红色来高亮显示。