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.

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.

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.

Sample Input 1

5 3
1 1 1 6 7

Sample Output 1

102

If you put the first and second slices on the first plate,
the third and fourth slices on the second plate, and
the fifth slice on the third plate,
we have (1+1)^{2}+(1+6)^{2}+7^2=102, so the unbalancedness is 102.
There is no way to put them to make the unbalancedness less than 102, so print 102.
Note that you cannot put the first, second, and third slices on the same plate.

Sample Input 2

2 1
167 924

Sample Output 2

1190281

Sample Input 3

12 9
22847 98332 854 68844 81080 46058 40949 62493 76561 52907 88628 99740

Sample Output 3

61968950639

见题面 Input 部分

见题面 Output 部分