Problem: 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.

Examples

Input

abcabcabc
1


Output

7


Input

atcodergrandcontest
3


Output

15

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define L long long
using namespace std;
int n,m,f[310][310][310];
char s[310];
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j,k,l;
	scanf("%s%d",s+1,&m);
	n=strlen(s+1);
	for(i=1;i<=n;i++)
	  for(j=0;j<=m;j++)
	    f[i][i][j]=1;
	for(l=1;l<n;l++)
	  for(i=1;i+l<=n;i++)
	    for(k=0;k<=m;k++)
	      {
           j=i+l;
           f[i][j][k]=max(max(f[i+1][j][k],f[i][j-1][k]),(s[i]==s[j]?f[i+1][j-1][k]:(k?f[i+1][j-1][k-1]:-1000000000))+2);
          }
    printf("%d\n",f[1][n][m]);
	return 0;
}