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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def dfs s,t,w
  max = w
  aa = ('a'..'z').to_a
  aa.each{|c|
    sd = s.index(c)
    td = t.index(c)
    if sd&&td
      res = dfs(s[sd+1..-1],t[td+1..-1],w+1)
      max = res if max < res
    end
  }
  return max
end

s = gets.chomp
t = s.reverse
k = gets.to_i
n = s.size

aa = ('a'..'z').to_a
inf = 10**9

res = dfs(s,t,0)

p [n, res+k*2].min