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>
using namespace std;
void chkmax(int &x,int y){
	x=x>y?x:y;
}
int dp[310][310][310];
int n,m;
char str[310];
int main(){
//	freopen("D.in","r",stdin);
	scanf("%s",str+1);
	n=strlen(str+1);
	scanf("%d",&m);
	for(int i=1;i<n;i++){
		if(str[i]==str[i+1])
			dp[i][i+1][0]=2;
		else{
			dp[i][i+1][0]=0;
			dp[i][i+1][1]=2;
		}
	}
	for(int i=1;i<=n;i++)
		dp[i][i][0]=1;
	for(int k=0;k<=m;k++){
		for(int l=0;l<n;l++){
			for(int i=1;i+l<=n;i++){
				int j=i+l;
				chkmax(dp[i][j][k+1],dp[i][j][k]);
				if(i>1)
					chkmax(dp[i-1][j][k],dp[i][j][k]);
				if(j<n)
					chkmax(dp[i][j+1][k],dp[i][j][k]);
				if(i>1&&j<n){
					if(str[i-1]==str[j+1])
						chkmax(dp[i-1][j+1][k],dp[i][j][k]+2);
					else
						chkmax(dp[i-1][j+1][k+1],dp[i][j][k]+2);
				}
			}
		}
	}
	printf("%d\n",dp[1][n][m]);
	return 0;
}