A14896. Subtract Operation

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 $k$ .

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 $2 \cdot 10^5$ .

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).

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 $\{5\}$ .