Binary Base Basics

 You are given a binary string 

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

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

Input Format

• The first line of input contains one integer T$T$, denoting the number of test cases. The description of T$T$ 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$N$ and K$K$, denoting the length of the binary string and the number of operations to be performed.
  • The second line contains the binary string S$S$.

Output Format

For each test case, print the answer on a new line — YES if the S$S$ can be made a palindrome using exactly K$K$ 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$1\le T\le 1000$
• 1≤N≤1000$1\le N\le 1000$
• 0≤K≤N$0\le K\le N$
• S$S$ is a binary string, i.e, contains only characters 0$0$ and 1$1$

Subtasks

Subtask #1 (100 points): Original constraints

Sample Input 1 

2
3 0
110
6 1
101100

Sample Output 1 

NO
YES

Explanation

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

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

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