Partition String into Palindromic Substrings

You are given a string S and a positive integer K. Your task is to determine if it is possible to partition S into exactly K non-empty substrings, such that each substring is a palindrome.

A palindrome is a string that reads the same forward and backward. Formally, a string substring is a palindrome if:

$substring = reverse(substring)$

The primary constraints are:

• If K > |S| (the length of S), then the answer is NO since you cannot partition the string into more substrings than its characters.
• Let $odd\_count$ be the number of characters in S that appear with an odd frequency. Then a necessary condition for the partition to be possible is that $odd\_count \leq K$.

If the conditions are met, output YES; otherwise, output NO.

Note: The input is provided via standard input (stdin) and the output should be printed to standard output (stdout).

inputFormat

The input consists of two lines:

1. The first line contains the string S consisting of lowercase English letters.
2. The second line contains an integer K representing the number of palindromic substrings to form.

outputFormat

Output a single line containing YES if it is possible to partition the string into K palindromic substrings, or NO otherwise.

## sample

aabb
2

YES