Problem:
Score : 1200 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

Imagine a game played on a line. Initially, the player is located at position 0 with N candies in his possession, and the exit is at position E. There are also N bears in the game. The i-th bear is located at x_i. The maximum moving speed of the player is 1 while the bears do not move at all.

When the player gives a candy to a bear, it will provide a coin after T units of time. More specifically, if the i-th bear is given a candy at time t, it will put a coin at its position at time t+T. The purpose of this game is to give candies to all the bears, pick up all the coins, and go to the exit. Note that the player can only give a candy to a bear if the player is at the exact same position of the bear. Also, each bear will only produce a coin once. If the player visits the position of a coin after or at the exact same time that the coin is put down, the player can pick up the coin. Coins do not disappear until collected by the player.

Shik is an expert of this game. He can give candies to bears and pick up coins instantly. You are given the configuration of the game. Please calculate the minimum time Shik needs to collect all the coins and go to the exit.

Constraints

1 \leq N \leq 100,000

1 \leq T, E \leq 10^9

0 < x_i < E

x_i < x_{i+1} for 1 \leq i < N

All input values are integers.

Partial Scores

In test cases worth 600 points, N \leq 2,000.

Input

The input is given from Standard Input in the following format:

N E T
x_1 x_2 ... x_N

Output

Print an integer denoting the answer.

Sample Input 1

3 9 1
1 3 8

Sample Output 1

12

The optimal strategy is to wait for the coin after treating each bear. The total time spent on waiting is 3 and moving is 9. So the answer is 3 + 9 = 12.

Sample Input 2

3 9 3
1 3 8

Sample Output 2

16

Sample Input 3

2 1000000000 1000000000
1 999999999

Sample Output 3

2999999996

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        int n, e, t;
        sc.Multi(out n, out e, out t);
        if (n > 5000) return;

        var x = sc.LongArr;
        var dp = new long[n + 1];
        dp[0] = 0;
        dp[1] = t;
        for (int i = 1; i < n; i++)
        {
            dp[i + 1] = Math.Min(dp[i] + x[i] - x[i - 1] + t, Math.Max((x[i] - x[0]) * 2, t) + x[i] - x[0]);
            for (int j = 0; j < i; j++)
            {
                dp[i + 1] = Math.Min(dp[i + 1], Math.Max((x[i] - x[j + 1]) * 2, t) + x[i] - x[j] + dp[j + 1]);
            }
        }
        sw.WriteLine(dp[n] + e - x[n - 1] + x[0]);
        sw.Flush();
    }
    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static T Max<T>(params T[] a) => a.Max();
    static T Min<T>(params T[] a) => a.Min();
    static void DBG<T>(params T[] a) => Console.WriteLine(string.Join(" ", a));
    static void DBG(params object[] a) => Console.WriteLine(string.Join(" ", a));
    static void Prt<T>(params T[] a) => sw.WriteLine(string.Join(" ", a));
    static void Prt(params object[] a) => sw.WriteLine(string.Join(" ", a));
}
class Score : IComparable
{
    int score, time;
    public int CompareTo(object obj)
    {
        var x = obj as Score;
        return this.score == x.score ? x.time.CompareTo(this.time) : this.score.CompareTo(x.score);
    }
}
static class ex
{
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
public static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class scanCHK : sc
{
    public static new string Str { get { var s = Console.ReadLine(); return s == s.Trim() ? s : ""; } }
}
class sc
{
    public static int Int => int.Parse(Str);
    public static long Long => long.Parse(Str);
    public static double Double => double.Parse(Str);
    public static string Str => Console.ReadLine().Trim();
    public static int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public static long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public static double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public static string[] StrArr => Str.Split();
    static bool eq<T, U>() => typeof(T).Equals(typeof(U));
    static T ct<T, U>(U inp) => (T)Convert.ChangeType(inp, typeof(T));
    static T cv<T>(string inp) => eq<T, int>() ? ct<T, int>(int.Parse(inp))
                         : eq<T, long>() ? ct<T, long>(long.Parse(inp))
                         : eq<T, double>() ? ct<T, double>(double.Parse(inp))
                         : eq<T, char>() ? ct<T, char>(inp[0])
                         : ct<T, string>(inp);
    public static void Multi<T>(out T a) => a = cv<T>(Str);
    public static void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public static void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
struct ModInt
{
    public static long Mod = 1000000007;
    long val;
    public ModInt(long v) { val = (v % Mod + Mod) % Mod; }

    public static implicit operator ModInt(long x) => new ModInt(x);
    public static explicit operator long(ModInt x) => x.val;

    public static ModInt operator+(ModInt x, ModInt y) => x.val + y.val;
    public static ModInt operator-(ModInt x, ModInt y) => x.val - y.val;
    public static ModInt operator*(ModInt x, ModInt y) => x.val * y.val;
    // must : gcd(y, Mod) == 1
    public static ModInt operator/(ModInt x, ModInt y) => x * ~y;
    // powmod(x, y, Mod);
    public static ModInt operator^(ModInt x, long y)
    {
        if (x.val == 0) return x;
        if (y == 0) return 1;
        var t = x ^ (y / 2);
        if ((y & 1) == 0) return t * t;
        return t * t * x;
    }

    public static ModInt operator-(ModInt x) => -(x.val);
    // inv(x) : x * inv(x) == 1
    // must : gcd(x, Mod) == 1
    public static ModInt operator~(ModInt x) => x ^ (Mod - 2);

    public override string ToString() => this.val.ToString();

    // public static bool operator==(ModInt x, ModInt y) => x.val == y.val;
    // public static bool operator!=(ModInt x, ModInt y) => x.val != y.val;
    // public override bool Equals(object obj) => obj != null && this.GetType() == obj.GetType() && this.val == ((ModInt)obj).val;
    // public override int GetHashCode() => (int)this.val;

}
class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n)
    {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static long[][] trans(long[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[m];
            for (int j = 0; j < m; j++) ret[i][j] = A[j][i];
        }
        return ret;
    }
    public static long[] mul(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b)
    {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) => pow(a, Mod - 2);
    public static long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y)
    {
        long g = a;
        x = 1;
        y = 0;
        if (b != 0)
        {
            g = extgcd(b, a % b, out y, out x);
            y -= a / b * x;
        }
        return g;
    }
    public static long lcm(long a, long b) => a * (b / gcd(a, b));
    public static long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++)
        {
            int piv = denom[p - 1];
            if (piv > 1)
            {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
}