Frog 3

Problem Statement

There are N stones, numbered 1, 2, …, N. For each i (1 ≤ i ≤ N), the height of Stone i is hi. Here, h1 < h2 < … < hN 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 (hj - hi)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 < … < hN ≤ 106

Input

Input is given from Standard Input in the following format:

N C
h1 h2 \ldots 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 135, 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 12458, the total cost incurred would be ((3 - 1)2 + 5) + ((5 - 3)2 + 5) + ((10 - 5)2 + 5) + ((13 - 10)2 + 5) = 62.


Compile Errors


							
Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 29
Your best score: 0
Source: Atcoder Educational DP Contest

Subtask Score
1 100
2 0