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 PYTHON3):

Solution:
import sys
readline = sys.stdin.readline

S = list(map(ord, readline().strip()))
N = len(S)
S = [None] + S + [None]
K = int(readline())

if N == 1:
    ans = 1
elif N == 2:
    ans = 1
    if S[1] == S[2]:
        ans = 2
    if K:
        ans = 2
else:
    dp1 = [[0]*(K+1) for _ in range(N+2)]
    dp2 = [[0]*(K+1) for _ in range(N+2)]
    for i in range(1, N+1):
        dp1[i][0] = 1
    for i in range(1, N):
        dp2[i][0] = 1
        if S[i] == S[i+1]:
            dp2[i][0] = 2    
        elif K:    
            dp2[i][1] = 2
    for s in range(3, N+1):
        dp3 = [[0]*(K+1) for _ in range(N+2)]
        for i in range(1, N-s+2):
            j = i+s-1    
            if S[i] == S[j]:
                for k in range(K+1):
                    dp3[i][k] = max(dp2[i+1][k], dp2[i][k], 2+dp1[i+1][k])
            else:
                dp3[i][0] = max(dp2[i+1][0], dp2[i][0], dp2[i+1][0])
                for k in range(1, K+1):
                    dp3[i][k] = max(dp2[i+1][k], dp2[i][k], dp1[i+1][k], 2+dp1[i+1][k-1])
        '''
        dp1 = [k[:] for k in dp2]
        dp2 = [k[:] for k in dp3]
        '''
        dp1 = dp2[:]
        dp2 = dp3[:]
    ans = max(dp3[1][k] for k in range(K+1))
print(ans)
'''
MLEした
dp = [[[0]*(K+1) for _ in range(N+2)] for _ in range(N+2)]
for i in range(1, N+1):
    dp[i][i][0] = 1
for i in range(1, N):
    dp[i][i+1][0] = 1
    if S[i] == S[i+1]:
        dp[i][i+1][0] = 2    
    elif K:    
        dp[i][i+1][1] = 2
for s in range(3, N+1):
    for i in range(1, N-s+2):
        j = i+s-1
        if S[i] == S[j]:
            for k in range(K+1):
                dp[i][j][k] = max(dp[i+1][j][k], dp[i][j-1][k], 2+dp[i+1][j-1][k])
        else:
            dp[i][j][0] = max(dp[i+1][j][0], dp[i][j-1][0], dp[i+1][j-1][0])
            for k in range(1, K+1):
                dp[i][j][k] = max(dp[i+1][j][k], dp[i][j-1][k], dp[i+1][j-1][k], 2+dp[i+1][j-1][k-1], dp[i+1][j-1][k])
print(max(dp[1][N][k] for k in range(K+1)))
'''