CF1917F.Construct Tree

普及/提高-

通过率：0%

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题目描述

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 $d$ .

输入格式

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 $2000$ .

输出格式

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).

输入输出样例

输入#1

3
4 10
1 2 3 4
4 7
1 4 3 4
6 18
2 4 3 7 6 7

输出#1

Yes
No
Yes

说明/提示

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.

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