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.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;

using CHTType = System.Int64;
public class ConvexHullTrick {
    private class Line {
        public readonly CHTType Slope;
        public readonly CHTType Intercept;

        public Line(CHTType slope, CHTType intercept) {
            Slope = slope;
            Intercept = intercept;
        }

        public CHTType Evaluate(CHTType x) {
            return Slope * x + Intercept;
        }
    }

    private readonly List<Line> _lines = new List<Line>();
    private readonly bool _isMin;

    public ConvexHullTrick(bool isMin = true) {
        _isMin = isMin;
    }

    // Add ax + b
    public void Add(CHTType a, CHTType b) {
        if (!_isMin) {
            a = -a;
            b = -b;
        }
        var line = new Line(a, b);

        while (_lines.Count >= 2 && IsUnnecessary(_lines[_lines.Count - 2], _lines[_lines.Count - 1], line)) {
            _lines.RemoveAt(_lines.Count - 1);
        }
        _lines.Add(line);
    }

    private static bool IsUnnecessary(Line l1, Line l2, Line l3) {
        return
            (l3.Intercept - l2.Intercept) * (l2.Slope - l1.Slope) >=
            (l2.Intercept - l1.Intercept) * (l3.Slope - l2.Slope);
    }

    public CHTType Get(CHTType x) {
        var best = CHTType.MaxValue;
        if (_lines.Count == 1) {
            best = _lines[0].Evaluate(x);
        } else {
            int lower = 0, upper = _lines.Count - 2;
            while (lower <= upper) {
                var mid = (lower + upper) >> 1;
                var y0 = _lines[mid].Evaluate(x);
                var y1 = _lines[mid + 1].Evaluate(x);
                if (y0 > y1) {
                    best = y1;
                    lower = mid + 1;
                } else {
                    best = y0;
                    upper = mid - 1;
                }
            }
        }
        return _isMin ? best : -best;
    }
}


internal partial class Solver {
    public void Run() {
        var n = ni();
        var c = nl();
        var h = ni(n);

        var cht = new ConvexHullTrick();
        var dp = new long[n];

        dp[0] = 0;
        for (var i = 1; i < n; i++) {
            // dp[i] = min_j (dp[j] + (h[i]-h[j])^2) + c
            //       = min_j (dp[j] + h[i]^2 - 2*h[i]*h[j] + h[j]^2) + c
            //       = min_j (dp[j] - 2*h[i]*h[j] + h[j]^2) + h[i]^2 + c
            //       = min_j (-2*h[i]*h[j] + dp[j] + h[j]^2 ) + h[i]^2 + c

            cht.Add(-2 * h[i - 1], dp[i - 1] + 1L * h[i - 1] * h[i - 1]);
            dp[i] = cht.Get(h[i]) + 1L * h[i] * h[i] + c;
        }

        cout.WriteLine(dp[n - 1]);
    }
}

// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#if LOCAL
        var inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

internal static class LinqPadExtension {
    [Conditional("DEBUG")]
    public static void Dump<T>(this T obj) {
#if DEBUG
        LINQPad.Extensions.Dump(obj);
#endif
    }
}

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return (int)NextLong(); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        var i = 0;
        var negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) {
                throw new FormatException();
            }
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        var array = new string[size];
        for (var i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        var array = new int[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        var array = new long[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        var array = new double[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new InvalidOperationException();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) {
                        break;
                    }
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}