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<iostream>
#include<cstdio>
#include<cstring>
const int N=305;
int dp[N][N][N]={},k;
char s[N];
int main() {
    scanf("%s%d",s+1,&k);int n=strlen(s+1);
    for(int i=1;i<=n;i++) for(int j=0;j<=k;j++) dp[i][i][j]=1,dp[i][i-1][j]=0;
    for(int j=1;j<n;j++) for(int i=1;i+j<=n;i++) for(int r=0;r<=k;r++){
        dp[i][i+j][r]=std::max(dp[i][i+j-1][r],dp[i+1][i+j][r]);
        if(s[i]==s[i+j]) dp[i][i+j][r]=std::max(dp[i][i+j][r],dp[i+1][i+j-1][r]+2);
        if(r) dp[i][i+j][r]=std::max(dp[i][i+j][r],dp[i+1][i+j-1][r-1]+2);
    }
    int ans=dp[1][n][k];
    for(int i=0;i<k;i++) ans=std::max(ans,dp[1][n][k]);
    printf("%d\n",ans);
    return 0;
}