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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace DP
{
    class Z
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int N = int.Parse(s[0]);
            long C = long.Parse(s[1]);
            List<long> h = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            List<long> costList = new List<long>();
            costList.Add(0);

            for (int i = 0; i < h.Count - 1; i++)
            {
                if (i == 0)
                {
                    long cost1 = (h[N - 1] - h[N - 2]) * (h[N - 1] - h[N - 2]) + C;
                    costList.Add(cost1);
                }
                else
                {
                    int k = N - i - 2;
                    long cmin = long.MaxValue;
                    for (int j = 1; j <= N; j++)
                    {
                        if (j > costList.Count) break;
                        int p = costList.Count - 1;
                        int m = k + j;
                        long cn = (h[k] - h[m])*(h[k]-h[m])+C;
                        long ch = costList[p - j + 1];
                        long cost = cn + ch;
                        if (cost < cmin) cmin = cost;
                    }
                    costList.Add(cmin);
                }
            }
            long ctotal = costList.Last();
            Console.WriteLine(ctotal);
        }

    }
}