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;

const int MX = 300;

char s[MX + 2];
int dp[MX + 2][MX + 2][MX + 1];

int main() {
	int k;
	ignore = scanf("%s %d", s + 1, &k);
	
	int n = strlen(s + 1);
	for (int l = n; l > 0; l--)
		for (int r = l; r <= n; r++)
			for (int p = 0; p <= k; p++) {
				if (s[l] == s[r]) {
					dp[l][r][p] = dp[l + 1][r - 1][p] + (l == r ? 1 : 2);
				}
				else {
					dp[l][r][p] = max(dp[l + 1][r][p], dp[l][r - 1][p]);
					if (p > 0) dp[l][r][p] = max(dp[l][r][p], dp[l + 1][r - 1][p - 1] + (l == r ? 1 : 2));
				}
			}
	
	printf("%d\n", dp[1][n][k]);
	
	return 0;
}