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A. Split it!

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKawashiro Nitori is a girl who loves competitive programming.

One day she found a string and an integer. As an advanced problem setter, she quickly thought of a problem.

Given a string $$$s$$$ and a parameter $$$k$$$, you need to check if there exist $$$k+1$$$ non-empty strings $$$a_1,a_2...,a_{k+1}$$$, such that $$$$$$s=a_1+a_2+\ldots +a_k+a_{k+1}+R(a_k)+R(a_{k-1})+\ldots+R(a_{1}).$$$$$$

Here $$$+$$$ represents concatenation. We define $$$R(x)$$$ as a reversed string $$$x$$$. For example $$$R(abcd) = dcba$$$. Note that in the formula above the part $$$R(a_{k+1})$$$ is intentionally skipped.

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1\le t\le 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case description contains two integers $$$n$$$, $$$k$$$ ($$$1\le n\le 100$$$, $$$0\le k\le \lfloor \frac{n}{2} \rfloor$$$) — the length of the string $$$s$$$ and the parameter $$$k$$$.

The second line of each test case description contains a single string $$$s$$$ of length $$$n$$$, consisting of lowercase English letters.

Output

For each test case, print "YES" (without quotes), if it is possible to find $$$a_1,a_2,\ldots,a_{k+1}$$$, and "NO" (without quotes) otherwise.

You can print letters in any case (upper or lower).

Example

Input

7 5 1 qwqwq 2 1 ab 3 1 ioi 4 2 icpc 22 0 dokidokiliteratureclub 19 8 imteamshanghaialice 6 3 aaaaaa

Output

YES NO YES NO YES NO NO

Note

In the first test case, one possible solution is $$$a_1=qw$$$ and $$$a_2=q$$$.

In the third test case, one possible solution is $$$a_1=i$$$ and $$$a_2=o$$$.

In the fifth test case, one possible solution is $$$a_1=dokidokiliteratureclub$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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