Description:
Vlad remembered that he had a series of $$$n$$$ tiles and a number $$$k$$$. The tiles were numbered from left to right, and the $$$i$$$-th tile had colour $$$c_i$$$.
If you stand on the first tile and start jumping any number of tiles right, you can get a path of length $$$p$$$. The length of the path is the number of tiles you stood on.
Vlad wants to see if it is possible to get a path of length $$$p$$$ such that:
- it ends at tile with index $$$n$$$;
- $$$p$$$ is divisible by $$$k$$$
- the path is divided into blocks of length exactly $$$k$$$ each;
- tiles in each block have the same colour, the colors in adjacent blocks are not necessarily different.
For example, let $$$n = 14$$$, $$$k = 3$$$.
The colours of the tiles are contained in the array $$$c$$$ = [$$$\color{red}{1}, \color{violet}{2}, \color{red}{1}, \color{red}{1}, \color{gray}{7}, \color{orange}{5}, \color{green}{3}, \color{green}{3}, \color{red}{1}, \color{green}{3}, \color{blue}{4}, \color{blue}{4}, \color{violet}{2}, \color{blue}{4}$$$]. Then we can construct a path of length $$$6$$$ consisting of $$$2$$$ blocks:
$$$\color{red}{c_1} \rightarrow \color{red}{c_3} \rightarrow \color{red}{c_4} \rightarrow \color{blue}{c_{11}} \rightarrow \color{blue}{c_{12}} \rightarrow \color{blue}{c_{14}}$$$
All tiles from the $$$1$$$-st block will have colour $$$\color{red}{\textbf{1}}$$$, from the $$$2$$$-nd block will have colour $$$\color{blue}{\textbf{4}}$$$.
It is also possible to construct a path of length $$$9$$$ in this example, in which all tiles from the $$$1$$$-st block will have colour $$$\color{red}{\textbf{1}}$$$, from the $$$2$$$-nd block will have colour $$$\color{green}{\textbf{3}}$$$, and from the $$$3$$$-rd block will have colour $$$\color{blue}{\textbf{4}}$$$.
Input Format:
The first line of input data contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$)—the number of tiles in the series and the length of the block.
The second line of each test case contains $$$n$$$ integers $$$c_1, c_2, c_3, \dots, c_n$$$ ($$$1 \le c_i \le n$$$) — the colours of the tiles.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output Format:
For each test case, output on a separate line:
- YES if you can get a path that satisfies these conditions;
- NO otherwise.
You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).
Note:
In the first test case, you can jump from the first tile to the last tile;
The second test case is explained in the problem statement.