You are given a binary string S and an integer K. In one operation, you can pick any bit and flip it, i.e turn 0 to 1 or 1 to 0. Can you make the string S a [palindrome] using exactly K operations?

Print YES if this is possible, and NO if it is not.

------ Input Format ------

• The first line of input contains one integer T, denoting the number of test cases. The description of T test cases follows.
• Each test case consists of two lines of input.
• The first line of each test case contains two space-separated integers N and K, denoting the length of the binary string and the number of operations to be performed.
• The second line contains the binary string S.

------ Output Format ------

For each test case, print the answer on a new line — YES if the S can be made a palindrome using exactly K operations, and NO otherwise.

You may print each character of YES and NO in either uppercase or lowercase (for example, yes, yEs, Yes will all be considered identical).

------ Constraints ------

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 1000$
$0 ≤ K ≤ N$
$S$ is a binary string, i.e, contains only characters $0$ and $1$

------ subtasks ------

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
2
3 0
110
6 1
101100

----- Sample Output 1 ------
NO
YES

----- explanation 1 ------
Test case $1$: $S$ is not a palindrome, and no operations can be performed on it because $K = 0$.

Test case $2$: Flip the first bit to obtain $S = 001100$, which is a palindrome.

见题面

见题面