Same Sum Subsequences#10962

Same Sum Subsequences

0.6 seconds

512 megabytes

Easy

You are given a string $s$ of length $n$ . You must perform the following operation exactly $k$ times: select any character in the string and remove it. After all operations, the string must be a palindrome.

Your task is to determine whether this is possible.

Input

The first line contains two integers $n$ and $k$ ( $1 \leq n \leq 1000$ 1 \leq n \leq 1000, $0 \leq k < n$ 0 \leq k < n) — the length of the string $s$ and the number of characters to remove.

The second line contains the string $s$ consisting of $n$ lowercase Latin letters.

Output

Output **YES** if it is possible to obtain a palindrome after removing exactly $k$ characters, otherwise output **NO**.

Examples

Example

5 2
abcba

YES

Example

4 2
abca

NO

Example 1