Subtract Operation

题意翻译

给定一个长度为 $n$ 的数列 $a$ 和一个整数 $k$，你可以对其进行 $n-1$ 次操作，每次操作选择数列中的一个数 $x$，然后将 $x$ 从数列中删除，并将剩下的所有数都减去 $x$。 请判断是否有一种操作序列，使得依次执行完该操作序列中的所有操作之后，数列中剩下的唯一一个数是 $k$。 数据范围： - $t$ 组数据，$1\leqslant t\leqslant 10^4$。 - $2\leqslant n,\sum n\leqslant 2\times 10^5$，$1\leqslant k\leqslant 10^9$。 - $-10^9\leqslant a_i\leqslant 10^9$。 Translated by Eason_AC

题目描述

You are given a list of $ n $ integers. You can perform the following operation: you choose an element $ x $ from the list, erase $ x $ from the list, and subtract the value of $ x $ from all the remaining elements. Thus, in one operation, the length of the list is decreased by exactly $ 1 $ . Given an integer $ k $ ( $ k>0 $ ), find if there is some sequence of $ n-1 $ operations such that, after applying the operations, the only remaining element of the list is equal to $ k $ .

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains two integers $ n $ and $ k $ ( $ 2 \leq n \leq 2\cdot 10^5 $ , $ 1 \leq k \leq 10^9 $ ), the number of integers in the list, and the target value, respectively. The second line of each test case contains the $ n $ integers of the list $ a_1, a_2, \ldots, a_n $ ( $ -10^9 \leq a_i \leq 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases is not greater that $ 2 \cdot 10^5 $ .

输出格式

For each test case, print YES if you can achieve $ k $ with a sequence of $ n-1 $ operations. Otherwise, print NO. You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as a positive answer).

输入输出样例

输入样例 #1

4
4 5
4 2 2 7
5 4
1 9 1 3 4
2 17
17 0
2 17
18 18

输出样例 #1

YES
NO
YES
NO

说明

In the first example we have the list $ \{4, 2, 2, 7\} $ , and we have the target $ k = 5 $ . One way to achieve it is the following: first we choose the third element, obtaining the list $ \{2, 0, 5\} $ . Next we choose the first element, obtaining the list $ \{-2, 3\} $ . Finally, we choose the first element, obtaining the list $ \{5\} $ .