Frog 3

Problem Statement

There are N stones, numbered 1, 2, …, N. For each i (1 ≤ i ≤ N), the height of Stone i is h_i. Here, h₁ < h₂ < … < 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, …, 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 ≤ N ≤ 2 × 10⁵
• 1 ≤ C ≤ 10¹²
• 1 ≤ h₁ < h₂ < … < h_N ≤ 10⁶

Input

Input is given from Standard Input in the following format:

N C
h1 h2 … hN

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.