Problem:
Score : 300 points

Problem Statement

In a public bath, there is a shower which emits water for T seconds when the switch is pushed.

If the switch is pushed when the shower is already emitting water, from that moment it will be emitting water for T seconds.
Note that it does not mean that the shower emits water for T additional seconds.

N people will push the switch while passing by the shower.
The i-th person will push the switch t_i seconds after the first person pushes it.

How long will the shower emit water in total?

Constraints

1 ≤ N ≤ 200,000

1 ≤ T ≤ 10^9

0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N ≤ 10^9

T and each t_i are integers.

Input

Input is given from Standard Input in the following format:

N T
t_1 t_2 ... t_N

Output

Assume that the shower will emit water for a total of X seconds. Print X.

Sample Input 1

2 4
0 3

Sample Output 1

7

Three seconds after the first person pushes the water, the switch is pushed again and the shower emits water for four more seconds, for a total of seven seconds.

Sample Input 2

2 4
0 5

Sample Output 2

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

Sample Input 3

4 1000000000
0 1000 1000000 1000000000

Sample Output 3

2000000000

Sample Input 4

1 1
0

Sample Output 4

1

Sample Input 5

9 10
0 3 5 7 100 110 200 300 311

Sample Output 5

67

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Globalization;
using System.IO;
using CodeChallenges;
using System.Diagnostics;

namespace CodeChallenges.Boilerplate.IO
{
    #region helpers
    class FormattedStreamWriter : StreamWriter { public FormattedStreamWriter(Stream stream) : base(stream) { } public FormattedStreamWriter(string filePath) : base(filePath) { } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } }
    static class IOExtensions
    {
        public static string ReadString(this StreamReader reader) { return reader.ReadToken(); }
        public static string[] ReadStringArray(this StreamReader reader, int n) { var array = new string[n]; for (int i = 0; i < n; ++i) { array[i] = reader.ReadToken(); } return array; }
        public static int ReadInt(this StreamReader reader) { return int.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static int[] ReadIntArray(this StreamReader reader, int n) { var array = new int[n]; for (int i = 0; i < n; ++i) { array[i] = int.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static uint ReadUnsignedInt(this StreamReader reader) { return uint.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static long ReadLong(this StreamReader reader) { return long.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static long[] ReadLongArray(this StreamReader reader, int n) { var array = new long[n]; for (int i = 0; i < n; ++i) { array[i] = long.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static ulong ReadUnsignedLong(this StreamReader reader) { return ulong.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static double ReadDouble(this StreamReader reader) { return double.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static double[] ReadDoubleArray(this StreamReader reader, int n) { var array = new double[n]; for (int i = 0; i < n; ++i) { array[i] = double.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static decimal ReadDecimal(this StreamReader reader) { return decimal.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static decimal[] ReadDecimalArray(this StreamReader reader, int n) { var array = new decimal[n]; for (int i = 0; i < n; ++i) { array[i] = decimal.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static void ResetBuffer() { buffer = new Queue<string>(1000); }
        static Queue<string> buffer = new Queue<string>(1000);
        static string ReadToken(this StreamReader reader) { while (buffer.Count == 0) { reader.ReadLine().Split(new[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).ToList().ForEach((t) => { buffer.Enqueue(t); }); } return buffer.Dequeue(); }
    }
    #endregion
}

#region launch
class Program
{
    static void Main(string[] args)
    {
#if SOLVER_ATWORKSPACE
        var run = true; var outputFile = "output.txt"; var inputFile = "input.txt";
        switch (args[0])
        {
            case "g": run = false; outputFile = "input.txt"; inputFile = "output.txt"; break;
            case "r":
            default: run = true; inputFile = "input.txt"; outputFile = "output.txt"; break;
        }
#endif

        using (var writer = new CodeChallenges.Boilerplate.IO.FormattedStreamWriter(
#if SOLVER_ATWORKSPACE
outputFile
#else
            Console.OpenStandardOutput()
#endif
))
        {
            using (var reader = new StreamReader(
#if SOLVER_ATWORKSPACE
inputFile
#else 
            Console.OpenStandardInput()
#endif
))
            {
#if SOLVER_ATWORKSPACE
                var stopw = new Stopwatch(); stopw.Start();
#endif
#if SOLVER_ATWORKSPACE
                if (run) new Solver(reader, writer).Do(); else new Generator(reader, writer).Create();

#else
                new Solver(reader, writer).Do();
#endif
#if SOLVER_ATWORKSPACE
                stopw.Stop(); writer.WriteLine("> {0}ms", stopw.ElapsedMilliseconds);
#endif
            }
        }
    }
}
#endregion

namespace CodeChallenges
{
    using CodeChallenges.Boilerplate.IO;

    public class Solver
    {
        private readonly StreamReader reader;
        private readonly StreamWriter writer;

        public Solver(StreamReader reader, StreamWriter writer)
        {
            this.reader = reader;
            this.writer = writer;
        }

        public void Do()
        {
            var n = reader.ReadInt();
            var T = reader.ReadInt();
            var t = reader.ReadIntArray(n);
            long time = 0;
            int end = T;
            for (int i = 1; i < n; ++i)
            {
                if (t[i] <= end)
                    time += t[i] - t[i - 1];
                else
                    time += end - t[i - 1];
                end = t[i] + T;
            }
            time += end - t[n - 1];
            writer.WriteLine(time);
        }
    }
}