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;
const int N = 300+5;
char s[N];
int f[N][N][N];
bool v[N][N][N];
inline int q(int l,int r,int k){
	if(r-l+1<=1)return r-l+1>=1;
	if(v[l][r][k])return f[l][r][k];
	v[l][r][k]=1;
	int diff = s[l]!=s[r];
	f[l][r][k]=max(q(l+1,r,k), q(l,r-1,k));
	if(k - diff>=0)f[l][r][k]=max(f[l][r][k],q(l+1,r-1,k-diff)+2);
	return f[l][r][k];
}

int main(){
	scanf("%s",s+1);
	int k;cin >> k;
	cout << q(1,strlen(s+1),k) << endl;
}