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 N 305
using namespace std;
char c[N];
int i,j,k,l,s,n,m,ans,f[N][N][N];
int main() {
	scanf("%s",c+1);
	n=strlen(c+1);
	scanf("%d",&m);
	for (i=1;i<=n;i++) f[i][i][0]=1;
	for (i=1;i<n;i++) {
		if (c[i]==c[i+1]) f[i][i+1][0]=2;
		else f[i][i+1][1]=2;
	}
	for (i=1;i<=n;i++) for (j=1;j+i-1<=n;j++) for (k=0;k<=m;k++) {
		int L=j-1,R=j+i;
		if (!f[L+1][R-1][k]) continue;
		if (L&&R<=n) {
			if (c[L]==c[R]) f[L][R][k]=max(f[L][R][k],f[L+1][R-1][k]+2);
			else if (k<m) f[L][R][k+1]=max(f[L][R][k+1],f[L+1][R-1][k]+2);
		}
		f[L+1][R][k]=max(f[L+1][R][k],f[L+1][R-1][k]);
		f[L][R-1][k]=max(f[L][R-1][k],f[L+1][R-1][k]);
	}
	for (i=0;i<=n;i++) for (j=1;j<=n+1;j++) for (k=0;k<=m;k++) ans=max(ans,f[i][j][k]);
	printf("%d\n",ans);
}