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 <iostream>
#include <string>
#include <algorithm>

using namespace std;

const int maxn = 301;
int dp[maxn][maxn][maxn] = {};

int main()
{
	string s;
	cin >> s;
	int n = s.length();
	int k;
	cin >> k;
	for (int t = 0; t <= k; t++)
		for (int l = 1; l <= n; l++)
			for (int r = n - 1; r >= l - 1; --r)
			{
				dp[l][r][t] = max(dp[l][r + 1][t], dp[l - 1][r][t]);
				if (s[l - 1] == s[r])
					dp[l][r][t] = max(dp[l][r][t], dp[l - 1][r + 1][t] + 2 - (int)(r == l - 1));
				if (t)
				{
					dp[l][r][t] = max(dp[l][r][t], dp[l][r][t - 1]);
					dp[l][r][t] = max(dp[l][r][t], dp[l - 1][r + 1][t - 1] + 2 - (int)(r == l - 1));
				}
			}
	int ans = 0;
	for (int i = 0; i < n; i++)
	{
		ans = max(ans, dp[i][i - 1][k]);
	}
	cout << ans;
	return 0;
}