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;

int dp[305][305][305];

int main(){
  
  string s;
  int K;
  
  cin>>s>>K;
  
  memset(dp,-1,sizeof(dp));
  
  dp[0][s.size()-1][0]=0;
  
  int ans=0;
  
  for(int l=0;l<s.size();l++)
    
    for(int r=s.size()-1;r>=l;r--){

      for(int k=0;k<=K;k++){
	
	if(dp[l][r][k]==-1) continue;
	
	if(s[l]==s[r]){
	  if(l==r) ans=max(ans, dp[l][r][k]+1);
	  else{
	    dp[l+1][r-1][k]=max(dp[l+1][r-1][k], dp[l][r][k]+2);
	    ans=max(ans, dp[l+1][r-1][k]);
	  }
	}
	
	if(l==r) continue;
	
	if(k<K){
	  dp[l+1][r-1][k+1]=max(dp[l+1][r-1][k+1], dp[l][r][k]+2);
	  ans=max(ans, dp[l+1][r-1][k+1]);
	}
	
	dp[l+1][r][k]=max(dp[l+1][r][k], dp[l][r][k]);
	dp[l][r-1][k]=max(dp[l][r-1][k], dp[l][r][k]);
	dp[l+1][r-1][k]=max(dp[l+1][r-1][k], dp[l][r][k]);
      }
    }
  
  cout<<ans<<endl;
  
  return 0;
}