Why Hobawoo Was Late for School 6

Hobawoo is almost at the Demon King's throne, but the door to the throne is locked and he cannot get in.

To open the door, a magic key of length $N$ must be turned into a magic key of length exactly $M$, and the power of the key must be made as large as possible.

A magic key of length $\ell$ has a sequence of $\ell$ non-negative integers $a_{1}, a_{2}, a_{3}, \cdots, a_{\ell}$. The power of the key is the sum of the numbers in the sequence.

For a key of length $\ell$, you can shorten it by applying one of the following 4 spells.

1. Remove $a_{1}$ and $a_{2}$, then add $a_{1}\oplus a_{2}$ to the front, producing a key of length $\ell-1$. The sequence changes as $(a_{1}, a_{2}, a_{3}, \cdots, a_{\ell}) \Rightarrow (a_{1}\oplus a_{2}, a_{3}, \cdots, a_{\ell})$.
2. Remove $a_{\ell-1}$ and $a_{\ell}$, then add $a_{\ell-1}\oplus a_{\ell}$ to the back, producing a key of length $\ell-1$. The sequence changes as $(a_{1}, \cdots, a_{\ell-2}, a_{\ell-1}, a_{\ell}) \Rightarrow (a_{1}, \cdots, a_{\ell-2}, a_{\ell-1}\oplus a_{\ell})$.
3. Remove $a_{1}, a_{2}, a_{3}, a_{4}$, then add $a_{2}\oplus a_{3}, a_{1}\oplus a_{4}$ to the front, producing a key of length $\ell-2$. The sequence changes as $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, \cdots, a_{\ell}) \Rightarrow (a_{2}\oplus a_{3}, a_{1}\oplus a_{4}, a_{5}, \cdots, a_{\ell})$.
4. Remove $a_{\ell-3}, a_{\ell-2}, a_{\ell-1}, a_{\ell}$, then add $a_{\ell-3}\oplus a_{\ell}, a_{\ell-2}\oplus a_{\ell-1}$ to the back, producing a key of length $\ell-2$. The sequence changes as $(a_{1}, \cdots, a_{\ell-4}, a_{\ell-3}, a_{\ell-2}, a_{\ell-1}, a_{\ell}) \Rightarrow (a_{1}, \cdots, a_{\ell-4}, a_{\ell-3}\oplus a_{\ell}, a_{\ell-2}\oplus a_{\ell-1})$.

The first line contains $N$ and $M$ separated by a space. ($4 \le M \le N \le 3\,000$)

The second line contains $N$ numbers $a_{1}, a_{2}, a_{3}, \cdots, a_{N}$ separated by spaces. ($0 \le a_{i} \le 10^{9}$)

Print the maximum power among the keys of length $M$ that can be made.

$\oplus$ is the bitwise XOR operation, applied bit by bit.

Bitwise XOR

• For each bit position of two numbers, the result bit is $1$ if the two bits differ, and $0$ if they are the same.
• Example:

$\begin{aligned} 0110_{2} &= 6 \\ \oplus \ 1100_{2} &= 12 \\ 1010_{2} &= 10 \end{aligned}$