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 (7.3.0) (judge verdict: Wrong Answer)

import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")



s = input()
K = int(input())
n = len(s)
dp = [[[0]*(K+1) for _ in range(n+1-i+1)] for i in range(n+1)]
for i in range(n):
    for j in range(K+1):
        dp[i][1][j] = 1
for l in range(2, n+1):
    for i in range(n-l+1):
        for k in range(K+1):
#             print(l, i, i+l, j)
            if s[i]==s[i+l-1]:
                dp[i][l][k] = dp[i+1][l-1][k] + 2
            else:
                dp[i][l][k] = max(dp[i+1][l][k], dp[i][l-1][k])
                if k>=1:
                    dp[i][l][k] = max(dp[i][l][k], dp[i+1][l-1][k-1]+2)
ans = max(dp[0][n][j] for j in range(K+1))
print(ans)