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: Wrong Answer)

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

/*
変更箇所は順読み逆読みの少なくとも片方で役立たないといけない
つまり1点分として加算される必要がある
逆に1点分以上の役割は持てない<-嘘だった
例えば右端の文字が他に存在しない文字ならそれを変更するのはOK
*/
int dp[400][400];

signed main(){
  string s;int K;cin>>s>>K;
  int N=s.size();
  string t=s;
  reverse(t.begin(),t.end());
  for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      dp[i+1][j+1]=max({dp[i+1][j],dp[i][j+1],dp[i][j]+(s[i]==t[j])});
    }
  }
  cout<<min(N,dp[N][N]+K*2)<<endl;
  //そんなわけない
}