CF2078A Final Verdict

[Testify - void (Mournfinale) feat. 星熊南巫](https://www.youtube.com/watch?v=xkUN_9HFNPg) 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. 1. $ 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] $ . 2. $ 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. 1. $ k = 1 $ and $ s_1 = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10] $ . Hence, $ a = [\operatorname{avg}(s_1)] = [10] $ .