Testify - void (Mournfinale) feat. 星熊南巫

You are given an array $$$a$$$ of length $$$n$$$, and must perform the following operation until the length of $$$a$$$ becomes $$$1$$$.

Choose a positive integer $$$k \lt |a|$$$ such that $$$\frac{|a|}{k}$$$ is an integer. Split $$$a$$$ into $$$k$$$ subsequences$$$^{\text{∗}}$$$ $$$s_1, s_2, \ldots, s_k$$$ such that:

Each element of $$$a$$$ belongs to exactly one subsequence.
The length of every subsequence is equal.

After this, replace $$$a = \left[ \operatorname{avg}(s_1), \operatorname{avg}(s_2), \ldots, \operatorname{avg}(s_k) \right] $$$, where $$$\operatorname{avg}(s) = \frac{\sum_{i = 1}^{|s|} s_i}{|s|}$$$ is the average of all the values in the subsequence. For example, $$$\operatorname{avg}([1, 2, 1, 1]) = \frac{5}{4} = 1.25$$$.

Your task is to determine whether there exists a sequence of operations such that after all operations, $$$a = [x]$$$.

$$$^{\text{∗}}$$$A sequence $$$x$$$ is a subsequence of a sequence $$$y$$$ if $$$x$$$ can be obtained from $$$y$$$ by the deletion of several (possibly, zero or all) elements.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$, $$$x$$$ ($$$1 \leq n, x \leq 100$$$) — the length of the array $$$a$$$ and the final desired value.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 100$$$) — the array $$$a$$$.

Output

For each test case, output "YES'" (without quotes) if there exists such a sequence of operations, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).

Note

In the first test case, $$$x = 3$$$ and $$$a = [3]$$$ already holds.

In the second test case, $$$x = 9$$$, and there exists no sequence of operations such that after all operations, $$$a = [9]$$$.

In the third test case, $$$x = 9$$$, and here is one possible sequence of operations.

$$$k = 2$$$, $$$s_1 = [1, 12, 8]$$$ and $$$s_2 = [9, 14, 10]$$$. Hence, $$$a = [\operatorname{avg}(s_1), \operatorname{avg}(s_2)] = [7, 11]$$$.
$$$k = 1$$$ and $$$s_1 = [7, 11]$$$. Hence, $$$a = [\operatorname{avg}(s_1)] = [9]$$$.

In the fourth test case, $$$x = 10$$$, and here is one possible sequence of operations.

$$$k = 1$$$ and $$$s_1 = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]$$$. Hence, $$$a = [\operatorname{avg}(s_1)] = [10]$$$.

Final Verdict

Examples