**Time limit:**1.00 s**Memory limit:**512 MB

Given an array of n elements, your task is to divide into k subarrays. The cost of each subarray is the square of the sum of the values in the subarray. What is the minimum total cost if you act optimally?

# Input

The first input line has two integers n and k: the array elements and the number of subarrays. The array elements are numbered 1,2,\dots,n.

The second line has n integers x_1,x_2,\dots,x_n: the contents of the array.

# Output

Print one integer: the minimum total cost.

# Constraints

- 1 \le k \le n \le 3000
- 1 \le x_i \le 10^5

# Example

Input:

8 3 2 3 1 2 2 3 4 1

Output:

110

Explanation: An optimal solution is [2,3,1], [2,2,3], [4,1], whose cost is (2+3+1)^2+(2+2+3)^2+(4+1)^2=110.