Hemose Shopping

题意翻译

给你两个数 $n, x$，代表有 $n$ 个元素。 然后输入 $n$ 个元素。 现在问你，能否通过交换两个距离大于等于 $x$ 的数，使得数组可以按照非递减的顺序来排序。 如果可以，输出 `YES`，否则，输出 `NO`。 注：$a$ 和 $b$ 的距离是：$ \lvert a - b \rvert$

题目描述

Hemose was shopping with his friends Samez, AhmedZ, AshrafEzz, TheSawan and O\_E in Germany. As you know, Hemose and his friends are problem solvers, so they are very clever. Therefore, they will go to all discount markets in Germany. Hemose has an array of $ n $ integers. He wants Samez to sort the array in the non-decreasing order. Since it would be a too easy problem for Samez, Hemose allows Samez to use only the following operation: - Choose indices $ i $ and $ j $ such that $ 1 \le i, j \le n $ , and $ \lvert i - j \rvert \geq x $ . Then, swap elements $ a_i $ and $ a_j $ . Can you tell Samez if there's a way to sort the array in the non-decreasing order by using the operation written above some finite number of times (possibly $ 0 $ )?

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ $ (1 \leq t \leq 10^5) $ . Description of the test cases follows. The first line of each test case contains two integers $ n $ and $ x $ $ (1 \leq x \leq n \leq 10^5) $ . The second line of each test case contains $ n $ integers $ a_1, a_2, ..., a_n $ $ (1 \leq a_i \leq 10^9) $ . It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case, you should output a single string. If Samez can sort the array in non-decreasing order using the operation written above, output "YES" (without quotes). Otherwise, output "NO" (without quotes). You can print each letter of "YES" and "NO" in any case (upper or lower).

输入输出样例

输入样例 #1

4
3 3
3 2 1
4 3
1 2 3 4
5 2
5 1 2 3 4
5 4
1 2 3 4 4

输出样例 #1

NO
YES
YES
YES

说明

In the first test case, you can't do any operations. In the second test case, the array is already sorted. In the third test case, you can do the operations as follows: - $ [5,1,2,3,4] $ , $ swap(a_1,a_3) $ - $ [2,1,5,3,4] $ , $ swap(a_2,a_5) $ - $ [2,4,5,3,1] $ , $ swap(a_2,a_4) $ - $ [2,3,5,4,1] $ , $ swap(a_1,a_5) $ - $ [1,3,5,4,2] $ , $ swap(a_2,a_5) $ - $ [1,2,5,4,3] $ , $ swap(a_3,a_5) $ - $ [1,2,3,4,5] $ (Here $ swap(a_i, a_j) $ refers to swapping elements at positions $ i $ , $ j $ ).