Palindrome Transformation with Exactly K Reversals

You are given a string S and an integer K. You need to determine if it is possible to transform the string into a palindrome by performing exactly K reversal operations on its substrings. A reversal operation means choosing any substring of S and reversing its characters.

There are two cases to consider:

• If S is already a palindrome, then performing an even number of reversals will keep it a palindrome. However, an odd number of reversals will spoil the symmetry.
• If S is not a palindrome, then you must perform enough reversals to fix the mismatches. In this problem, it is guaranteed that if K is greater than or equal to the length of S (i.e. $$K \geq |S|$$), then the transformation is always possible.

Your task is to output "Yes" if the transformation is possible using exactly K reversals, and "No" otherwise.

inputFormat

The first line contains an integer T denoting the number of test cases. Each of the following T lines contains a string S and an integer K separated by a space.

outputFormat

For each test case, output a single line with the answer "Yes" if the transformation is possible with exactly K reversals, or "No" otherwise.

## sample

5
abcba 2
abccba 1
racecar 1
abcdefg 0
abc 3

Yes
No
No
No
Yes

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