Palindromic Strings
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  Difficulty: Medium   Marks: 4

Given a string you have to transform it into a palindrome . In order to acheive that you have to perform exactly k insertion of characters(you cannot perform any more or less number of insertions).Now you have to report whether the string can be converted to a palindrome by making exactly k insertions.
 

Input :
The first line contains the number of test cases T. For each test case the first line contains the length of the string N and the number of insertions k. The second line contains the string S.

 

Output :
For each test case, print "YES"(without quotes) if the string can be converted to a palindrome making exactly k insertions otherwise "NO"(without quotes).

 

Constraints :

1 ≤ T ≤ 100

0<=k<=100000

The string consists of only lower case English Alphabets (a-z).
 

Example:

Input :

2

4 2

abac

5 3

abcde

Output :

YES

NO

 

Explanation :

For the first test case abac can be transformed to cabbac (which is palindrome) adding two characters c and b.

For the second test case abcde cannot be transformed to palindrome using 3 insertions.

For the third test case ab can be transformed to cabac (which is palindrome) adding three characters a, c and c.
 

** For More Input/Output Examples Use 'Expected Output' option **

Author: Arnab Deb


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