Forming a Nearly Palindrome

You are given a string s of length n and an integer m. Your task is to determine whether it is possible to rearrange the characters of s and remove at most m characters so that the resulting string becomes a palindrome.

A palindrome is a string that reads the same forward and backward. In order to form a palindrome, at most one character can appear an odd number of times. Formally, if we denote the number of characters that have an odd frequency as odd_count, then the minimum number of removals needed to form a palindrome is given by:

$$\max(0,\; odd\_count - 1)$$

If this minimum number of removals is less than or equal to m, then it is possible to form a palindrome, and you should output YES; otherwise, output NO.

Note: You are allowed to rearrange the string arbitrarily before making removals.

inputFormat

The first line contains an integer T representing the number of test cases. Each test case consists of a single line containing an integer n (the length of the string), a string s of length n, and an integer m, separated by spaces.

For example:

4
5 abcbc 1
3 aaab 1
6 racecar 0
4 abcda 1

outputFormat

For each test case, output a single line containing either YES if it is possible to rearrange the string and remove at most m characters to form a palindrome, or NO otherwise.

## sample

4
5 abcbc 1
3 aaab 1
6 racecar 0
4 abcda 1

YES
YES
YES
NO

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