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 pb push_back
#define mp make_pair
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
const int N = 100000 + 100;
const int MOD = 1000000007;
const int oo = 1e9;

string s;
int k,dp[301][301][301];

int calc(int l , int r , int rem){
	if(rem<0)return -oo;
	if(l==r)return 1;
	if(l>r)return 0;
	int &ret = dp[l][r][rem];
	if(ret != -1)return ret;
	ret = max(calc(l+1,r,rem),calc(l,r-1,rem));
	if(s[l]==s[r])
		ret = max(ret,2+calc(l+1,r-1,rem));
	if(s[l]!=s[r])
		ret = max(ret,2+calc(l+1,r-1,rem-1));
	return ret;
}
int main() {
	memset(dp,-1,sizeof dp);
	cin >> s>>k;
	cout << calc(0,s.size()-1,k) << endl;
	return 0;
}