A. Final Verdict
math
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 \(k < |a|\) 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.
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 \(a\).
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).
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, \(a = [\operatorname{avg}(s_1)] = [10]\).