A16156 | Tiles Comeback

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 $\color{blue}{\textbf{4}}$ .

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 $2 \cdot 10^5$ .

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).