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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int dp[400][400][400];

int main() {
  string s;
  cin >> s;

  int K;
  cin >> K;

  for (int i = 0; i < s.size(); ++i) {
    dp[i][i][0] = 1;
  }

  int ans = 1;
  for (int d = 1; d < s.size(); ++d) {
    for (int l = 0; l + d < s.size(); ++l) {
      int r = l + d;
      for (int k = 0; k <= K; ++k) {
        if (s[l] == s[r]) {
          dp[l][r][k] = max(dp[l][r][k], dp[l + 1][r - 1][k] + 2);
        } else {
          if (k) dp[l][r][k] = max(dp[l][r][k], dp[l + 1][r - 1][k - 1] + 2);
        }

        dp[l][r][k] = max({dp[l][r][k], dp[l + 1][r][k], dp[l + 1][r - 1][k], dp[l][r - 1][k]});
        ans = max(ans, dp[l][r][k]);
      }
    }
  }

  cout << ans << endl;
}