An Amazon fulfillment center has n orders arranged in a fixed line.

The reward for processing order i is a_i.

The manager wants to process exactly k orders.

Normally, no two selected orders can be adjacent. However, the manager has one special override.

The override allows at most one adjacent selected pair in the final selection.

Your task is to find the maximum total reward possible by selecting exactly k orders with at most one adjacent selected pair.

If it is impossible to select exactly k valid orders, print -1.

The first line contains two integers KaTeX can only parse string typed expression and KaTeX can only parse string typed expression — the number of orders and the number of orders to select.

The second line contains KaTeX can only parse string typed expression integers KaTeX can only parse string typed expression — the reward of each order.

Print a single integer — the maximum total reward possible. If it is impossible to select exactly KaTeX can only parse string typed expression valid orders, print KaTeX can only parse string typed expression.