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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void solve()
    {
        int N = cin.nextint;
        var C = cin.nextlong;
        var dp = new long[N];
        var CHT = new ConvexHullTrick(N);
        var H = cin.scanlong;
        CHT.Add(-2 * H[0], H[0] * H[0]);
        for (int j = 1; j < N; j++)
        {
            dp[j] = H[j] * H[j] + C + CHT.Query(H[j]);
            CHT.Add(-2 * H[j], dp[j] + H[j] * H[j]);
        }
        WriteLine(dp[N - 1]);
        //dp.join();
    }

}

/// <OriginalAuthor>蟻本</OriginalAuthor>
class ConvexHullTrick
{
    class Linear
    {
        public long a, b;
        public Linear(long a, long b) { this.a = a; this.b = b; }
    }
    /// <summary>
    /// 区間が[s, t)のデック
    /// </summary>
    readonly Linear[] deq;
    int s, t;

    /// <summary>
    /// 追加される直線の係数が単調減少であるCHTのインスタンス
    /// </summary>
    /// <param name="N">直線の最大数</param>
    public ConvexHullTrick(int N)
    {
        deq = new Linear[N];
        s = 0; t = 0;
    }

    /// <summary>
    /// f(x)を計算
    /// </summary>
    /// <param name="f"></param>
    /// <param name="x"></param>
    /// <returns>long値</returns>
    long f(Linear f, long x)
    {
        return f.a * x + f.b;
    }
    /// <summary>
    /// f2が最小値をとる可能性があるか判定 f1.a >= f2.a >= f3.a
    /// </summary>
    /// <param name="f1"></param>
    /// <param name="f2"></param>
    /// <param name="f3"></param>
    /// <returns>可能性がなければ true</returns>
    bool check(Linear f1, Linear f2, Linear f3)
    {
        return (f2.a - f1.a) * (f3.b - f2.b) >= (f2.b - f1.b) * (f3.a - f2.a);
    }

    /// <summary>
    /// 直線をデックに追加
    /// </summary>
    /// <param name="a">単調減少となる傾きa</param>
    /// <param name="b">切片b</param>
    public void Add(long a, long b)
    {
        var f = new Linear(a, b);
        // 末尾から最小値を取る可能性がなくなったものを取り除く
        while (s + 1 < t && check(deq[t - 2], deq[t - 1], f)) t--;
        deq[t++] = f;
    }
    /// <summary>
    /// f(x)の最小値を計算
    /// </summary>
    /// <param name="x">単調増加となるx</param>
    /// <returns>long値</returns>
    public long Query(long x)
    {
        // 先頭が最小値でなければ取り除く
        while (s + 1 < t && f(deq[s], x) >= f(deq[s + 1], x)) s++;
        return f(deq[s], x);
    }
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}