Problem:
Score : 900 points

Problem Statement

Takahashi has decided to give a string to his mother.

The value of a string T is the length of the longest common subsequence of T and T', where T' is the string obtained by reversing T.
That is, the value is the longest length of the following two strings that are equal: a subsequence of T (possibly non-contiguous), and a subsequence of T' (possibly non-contiguous).

Takahashi has a string S. He wants to give her mother a string of the highest possible value, so he would like to change at most K characters in S to any other characters in order to obtain a string of the highest possible value.
Find the highest possible value achievable.

Constraints

1 \leq |S| \leq 300

0 \leq K \leq |S|

S consists of lowercase English letters.

K is an integer.

Input

Input is given from Standard Input in the following format:

S
K

Output

Print the highest possible value achievable.

Sample Input 1

abcabcabc
1

Sample Output 1

7

Changing the first character to c results in cbcabcabc.
Let this tring be T, then one longest common subsequence of T and T' is cbabcbc, whose length is 7.

Sample Input 2

atcodergrandcontest
3

Sample Output 2

15

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys

readline = sys.stdin.buffer.readline

ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))

def solve():
  s = list(ns())
  ls = len(s)
  lk = ni()
  dp = [[[0]*(lk+1) for _ in range(ls)] for i in range(ls)]
  for i in range(ls):
    dp[i][i][0] = 1
  for k in range(lk+1):
    for dis in range(1, ls):
      for i in range(ls - dis):
        j = i + dis
        if s[i] == s[j]:
          dp[i][j][k] = dp[i+1][j-1][k] + 2
        elif k:
          dp[i][j][k] = dp[i+1][j-1][k-1] + 2
        dp[i][j][k] = max(dp[i][j][k], dp[i+1][j][k], dp[i][j-1][k])

  print(max(dp[0][ls-1]))
  return

solve()