Problem:
Score : 100 points

Problem Statement

There are N stones, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), the height of Stone i is h_i.
Here, h_1 < h_2 < \cdots < h_N holds.

There is a frog who is initially on Stone 1.
He will repeat the following action some number of times to reach Stone N:

If the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \ldots, N. Here, a cost of (h_j - h_i)^2 + C is incurred, where j is the stone to land on.

Find the minimum possible total cost incurred before the frog reaches Stone N.

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

1 \leq C \leq 10^{12}

1 \leq h_1 < h_2 < \cdots < h_N \leq 10^6

Input

Input is given from Standard Input in the following format:

N C
h_1 h_2 \ldots h_N

Output

Print the minimum possible total cost incurred.

Sample Input 1

5 6
1 2 3 4 5

Sample Output 1

20

If we follow the path 1 → 3 → 5, the total cost incurred would be ((3 - 1)^2 + 6) + ((5 - 3)^2 + 6) = 20.

Sample Input 2

2 1000000000000
500000 1000000

Sample Output 2

1250000000000

The answer may not fit into a 32-bit integer type.

Sample Input 3

8 5
1 3 4 5 10 11 12 13

Sample Output 3

62

If we follow the path 1 → 2 → 4 → 5 → 8, the total cost incurred would be ((3 - 1)^2 + 5) + ((5 - 3)^2 + 5) + ((10 - 5)^2 + 5) + ((13 - 10)^2 + 5) = 62.

Solution in Python (3.8.2) (judge verdict: Accepted)

from collections import deque


def F(x, p, q):
    return x * p + q


def check(f1, f2, f3):
    a1, b1 = f1
    a2, b2 = f2
    a3, b3 = f3
    return (a2 - a1) * (b3 - b2) >= (b2 - b1) * (a3 - a2)


def main():
    N, C = map(int, input().split())
    H = list(map(int, input().split()))

    dp = 0
    line = deque()
    line.append((-2 * H[0], H[0] ** 2))
    i = 0

    for h in H[1:]:
        while i + 1 < len(line) and F(h, *line[i]) >= F(h, *line[i + 1]):
            i += 1
        dp = h ** 2 + C + F(h, *line[i])

        p = -2 * h
        q = h ** 2 + dp
        while len(line) >= 2 and check(line[-2], line[-1], (p, q)):
            line.pop()
        line.append((p, q))

    print(dp)


if __name__ == "__main__":
    main()