CF2124D Make a Palindrome

You are given an array $ a $ of size $ n $ , and an integer $ k $ . You may perform the following operation any number of times: - Select two integers $ l $ and $ r $ $ (1 \le l \le r \le |a|) $ such that $ r-l+1 \geq k $ . - Then, select an index $ i $ such that $ l\leq i \leq r $ where $ a_i $ is the $ k $ -th smallest number out of the subarray $ [a_l,a_{l+1},\ldots,a_r] $ . If there are multiple possible $ i $ , you may select any. For example, consider $ a = [1, 2, 2, 1, 3], l = 1, r = 5 $ and $ k = 3 $ , the possible candidates of $ i $ are indices $ 2 $ and $ 3 $ . - Then, delete $ a_i $ from $ a $ , concatenating the remaining parts of the array. Determine if it is possible to get an array that is a palindrome $ ^{\text{∗}} $ after any number of operations. Note that an empty array is considered a palindrome. $ ^{\text{∗}} $ An array $ b=[b_1,b_2,\ldots,b_m] $ is a palindrome if for each $ 1 \leq i \leq m $ , $ b_i=b_{m+1-i} $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line contains two integers $ n $ and $ k $ ( $ 1 \leq k \leq n \leq 2\cdot 10^5 $ ). The second line contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 1 \leq a_i \leq n $ ) — denoting the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output YES if it is possible to create a palindrome, and NO otherwise. You can output in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

In the first test case, $ a $ is already a palindrome. In the second test case, we can perform two operations as follows: $ [\mathbf{1,1},2,1]\rightarrow [1,\mathbf{2},1]\rightarrow[1,1] $ In the third test case, we can perform one operation as follows: $ [\mathbf{2,3,4,5,3,2}]\rightarrow[2,3,4,3,2] $ . In the fourth and fifth test cases, it can be shown it is impossible to create a palindrome no matter what operations are used.