Description

Original Problem from: HDU 3507

Given $N$ words, each with a non-negative weight $C_i$, they are to be divided into consecutive segments. The cost of each segment is the square of the sum of the weights of the words in the segment plus a constant $M$, i.e., $(\sum C_i)^2 + M$. The goal is to find an optimal segmentation that minimizes the total cost.

Input Format

The input contains multiple test cases. For each test case:
The first line contains two integers $N$ and $M$.
The second line contains $N$ integers.

Output Format

Output a single integer representing the minimum total cost.

Sample 1

5 5
5 9 5 7 5

230

Constraints & Notes

For all test cases, $0\le N\le 5\times 10^5,\ 0\le M\le 1000$.