Problem Statement

We have $N$ slices of toast and $M$ plates. $M$ is an integer between $\frac{N}{2}$ and $N$, inclusive. The $i$-th slice of toast has a deliciousness of $A_{i}$.

Let us put the $N$ slices of toast on the $M$ plates to satisfy the following two conditions.

• Each plate can have at most two slices of toast on it.
• Every slice of toast is on some plate.

Let $B_{j}$ be the sum of the deliciousness of the toast on the $j$-th plate ($0$ if the plate has no toast on it). Then, let the unbalancedness be $\sum_{j=1}^{M} B_{j}^{2}$.

Find the minimum possible value of the unbalancedness.

Constraints

• $1\leq N\leq 2\times 10^{5}$
• $\frac{N}{2}\leq M\leq N$
• $1\leq A_{i}\leq 2\times 10^{5}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
A_{1} A_{2} \cdots A_{N}

Output

Print the answer.