P14627 [2018 KAIST RUN Fall] Fascination Street

A street named $\textit{Fascination Street}$ is divided into $N$ equal length of blocks. For each block $i$ ($1 \leq i \leq N$), it has block $i-1$ in its left side if $i > 1$, and block $i+1$ in its right side if $i < N$. Unlike its name, the street is infamous to be a dark and eerie place in the night. To solve this, Robert decided to install the streetlight for some of the blocks. The cost of installing a streetlight for $i$-th block is $W_i$, and the total cost is the sum of each installation cost. After installing, every block should either have a streetlight, or have a streetlight in it's left or right block. Robert also has some tricks to reduce the cost. Before installing the streetlight, Robert selects two distinct blocks $i$ and $j$, and exchange their position. After the operation, the cost of installation is exchanged. In other words, the operation simply swaps the value of $W_i$ and $W_j$. This operation have no cost, but Robert can only perform it at most $K$ times. Now, given the array $W$ and the maximum possible number of operations $K$, you should find the minimum cost of lighting the whole street.

The first line contains two space-separated integers $N, K$. $N$ is the number of blocks, and $K$ is the maximum possible number of operations. ($1 \leq N \leq 250000 , 0 \leq K \leq 9$) The second line contains $N$ space-separated integers $W_1, W_2 \cdots W_N$, where $W_i$ is the cost of installing a streetlight for $i$-th block. ($0 \leq W_i \leq 10^9$)

Print a single integer which contains the minimum cost of lighting the whole street.