OR Score of a Sequence

You are given a sequence $A$ of size $N$ and an integer $K$. Split the sequence into $K$ contiguous non-empty groups. Every element of the sequence must belong to exactly one group.

Each group is written as two integers $L$ and $R$, meaning that the $L$-th number through the $R$-th number belong to that group. The score of a group is the bitwise OR of every element in it.

The OR score of the sequence is the sum of the scores of all groups.

Write a program that splits the sequence into $K$ contiguous non-empty groups and finds the maximum OR score of the sequence.

The first line contains $N$ and $K$. ($1 \le N \le 5\,000$, $1 \le K \le N$)

The second line contains the elements of the sequence $A_1, A_2, \dots, A_N$, separated by spaces. ($0 \le A_i \le 2^{30}$)

Print the maximum OR score of the sequence.

In the first example, splitting into $(1, 2)$ and $(2)$ scores $(1 \text{ OR } 2) + 2 = 3 + 2 = 5$.

In the second example, splitting into $(1, 2)$, $(3)$, $(4)$ scores $(1 \text{ OR } 2) + 3 + 4 = 3 + 3 + 4 = 10$.

In the third example, the only possible split is $(1)$ and $(2)$.