CF1867D.Cyclic Operations

Egor has an array $a$ of length $n$, initially consisting of zeros. However, he wanted to turn it into another array $b$ of length $n$.

Since Egor doesn't take easy paths, only the following operation can be used (possibly zero or several times):

• choose an array $l$ of length $k$ ($1 \leq l_i \leq n$, all $l_i$ are distinct) and change each element $a_{l_i}$ to $l_{(i\%k)+1}$ ($1 \leq i \leq k$).

He became interested in whether it is possible to get the array $b$ using only these operations. Since Egor is still a beginner programmer, he asked you to help him solve this problem.

The operation $\%$ means taking the remainder, that is, $a\%b$ is equal to the remainder of dividing the number $a$ by the number $b$.

叶戈尔有一个长度为 $n$ 的数组 $a$，初始时所有元素均为 $0$。但他希望将其变为另一个长度为 $n$ 的数组 $b$。

由于叶戈尔从不走捷径，他只允许使用以下操作（可执行零次或多次）：

• 选择一个长度为 $k$ 的数组 $l$（满足 $1 \leq l_i \leq n$，且所有 $l_i$ 互不相同），并将每个元素 $a_{l_i}$ 修改为 $l_{(i\%k)+1}$（其中 $1 \leq i \leq k$）。

他开始好奇：仅通过这些操作，是否可能得到数组 $b$？由于叶戈尔仍是一名初学编程者，他请你帮助他解决这个问题。

运算符 $\%$ 表示取模运算，即 $a\%b$ 表示 $a$ 除以 $b$ 所得的余数。

The first line of the input contains an integer $t$ ($1 \leq t \leq 10^5$) - the number of test cases.

Each test case consists of two lines. The first line contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 10^5$).

The second line contains the array $b_1, b_2, \ldots, b_n$ ($1 \leq b_i \leq n$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \leq t \leq 10^5$），表示测试用例的数量。

每个测试用例由两行组成。第一行包含两个整数 $n$ 和 $k$（$1 \leq k \leq n \leq 10^5$）。

第二行包含数组 $b_1, b_2, \ldots, b_n$（$1 \leq b_i \leq n$）。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

For each test case, output "YES" (without quotes) if there is a way to get the array $b$ using only the given operation. Otherwise, output "NO" (without quotes). You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes" and "YES" will be accepted as a positive answer.

对于每个测试用例，如果仅使用给定操作就能得到数组 $b$，则输出 "YES"（不带引号）；否则输出 "NO"（不带引号）。每个字母可为任意大小写（小写或大写）。例如，字符串 "yEs"、"yes"、"Yes" 和 "YES" 均被视为正确的肯定回答。

Let's consider the first example:

• Apply the operation with $l$ = $[1,2,3]$. Now $a$ = $[2,3,1,0,0]$.
• Apply the operation with $l$ = $[3,5,4]$. Now $a$ = $[2,3,5,3,4]$ = $b$.

We see that it is possible to get the array $b$. Therefore, the answer is YES.

In the second example, it can be proven that the array $b$ cannot be obtained, therefore the answer is NO.

我们考虑第一个例子：

• 对 $l = [1,2,3]$ 执行该操作。此时 $a = [2,3,1,0,0]$。
• 对 $l = [3,5,4]$ 执行该操作。此时 $a = [2,3,5,3,4] = b$。

我们发现可以得到数组 $b$。因此，答案是 YES。

在第二个例子中，可以证明无法得到数组 $b$，因此答案是 NO。