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 <algorithm>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
int n,m,i,j,dp[305][305][305],vis[305][305];
string st;
void dfs(int l,int r)
{
	if (l>r) return;
	if (vis[l][r]) return;
	vis[l][r]=1;
	if (l==r)
	{
		fill(dp[l][r],dp[l][r]+m+1,1);
		return;
	}
	int i;
	dfs(l+1,r-1);
	dfs(l+1,r);
	dfs(l,r-1);
	for (i=0;i<=m;i++)
	{
		dp[l][r][i]=0;
		if (st[l]==st[r]) dp[l][r][i]=max(dp[l][r][i],dp[l+1][r-1][i]+2);
		else
		{
			if (i) dp[l][r][i]=max(dp[l][r][i],dp[l+1][r-1][i-1]+2);
			dp[l][r][i]=max(dp[l][r][i],dp[l+1][r][i]);
			dp[l][r][i]=max(dp[l][r][i],dp[l][r-1][i]);
		}
	}
}
int main()
{
	cin>>st>>m;
	st=" "+st;
	dfs(1,st.size()-1);
	cout<<dp[1][st.size()-1][m]<<endl;
	return 0;
}