Palindrome Transformation

You are given a string s and two non-negative integers m and n. You are allowed to remove at most m characters from s and add at most n characters to s. Determine whether it is possible to rearrange s (after the modifications) into a palindrome.

A palindrome is a string that reads the same forward and backward. A necessary condition for a string to be rearranged into a palindrome is that at most one character can have an odd frequency. In this problem, you are permitted to modify the string in order to achieve this condition.

The condition to check can be expressed in LaTeX as follows:

$$\text{odd\_count} \le m + 2n + 1,$$

where odd_count represents the number of characters in s that appear an odd number of times.

inputFormat

The input consists of a single line containing a string s followed by two space-separated integers m and n.

Constraints:

• s consists of lowercase English letters only.
• m and n are non-negative integers.

outputFormat

Output a single line containing either YES if it is possible to rearrange the adjusted string into a palindrome, or NO otherwise.

## sample

abac 1 1

YES