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:
def get_ind(l, r):
    mod = 3
    return OFFSET * (l % mod) + r

s = input()
n = len(s)
k = int(input())

dp = [[0] * ((n + 1) * 3) for i in range(k + 1)]
OFFSET = n + 1

# 長さ1のときの初期化
for i in range(n):
    dp[0][get_ind(i, i + 1)] = 1

# 長さ2~nのときのDP
for length in range(2, n + 1):
    for l in range(n + 1):
        for ki in range(k + 1):
            r = l + length
            if r > n:
                break
            if s[l] == s[r - 1]:
                dp[ki][get_ind(l, r)] = max(2 + dp[ki][get_ind(l + 1, r - 1)], dp[ki][get_ind(l, r)])
            else:
                dp[ki][get_ind(l, r)] = max(dp[ki][get_ind(l + 1, r)], dp[ki][get_ind(l, r - 1)], dp[ki][get_ind(l, r)])
                if ki - 1 >= 0:
                    dp[ki][get_ind(l, r)] = max(dp[ki - 1][get_ind(l + 1, r - 1)] + 2, dp[ki][get_ind(l, r)])

ans = 0
for i in range(k + 1):
    for j in range(3 * (n + 1)):
        ans = max(ans, dp[i][j])
print(ans)