A street named 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 $$$i \gt 1$$$, and block $$$i+1$$$ in its right side if $$$i \lt N$$$.

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.