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

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

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.

Idx	Name	Rating
A	Escalator Conversations	800
B	Parity Sort	800
C	Tiles Comeback	1000
D	Prefix Permutation Sums	1300
E	Nastya and Potions	1500
F	Lisa and the Martians	1800
G	Vlad and the Mountains	2000

Codeforces Round 888 (Div. 3)