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.Text;
using System.Linq;

namespace codeTester.todayProblem
{
    class ABC060C
    {
        static List<long> nt = new List<long>();
        static List<long> tList = new List<long>();
        static long answer = 0;

        static long T_N_MAX = 1000000000;
        static long T_MAX = 1000000000;

        public static void Main(string[] args)
        {
            Input();
            Logic();
            Output();
        }

        static void Input()
        {
            nt = ReadSpaceSeparatedValues();
            tList = ReadSpaceSeparatedValues();
        }

        public static List<long> ReadSpaceSeparatedValues()
        {
            List<long> values = new List<long>();
            string[] inputs = Console.ReadLine().Split(' ');
            foreach (string input in inputs)
            {
                values.Add(long.Parse(input));
            }

            return values;
        }

        static void Logic()
        {
            long n = nt[0];
            long t = nt[1];
            List<long> tShiftList = tList.Select(n0 => n0).ToList();
            tShiftList.RemoveAt(0);
            tShiftList.Add(T_N_MAX + T_MAX);
            answer = tList.Zip(tShiftList, (n1, n2) => n2 - n1).Aggregate((long)0, (sum, value) => sum + Math.Min(t, value));
        }

        static void Output()
        {
            Console.WriteLine(answer.ToString());
        }

        static void DebugPrint(string msg)
        {
            // 提出時に消す
            // Console.WriteLine(msg);
        }

        static void DebugPrint(string msg, List<long> values)
        {
            // 提出時に消す
            DebugPrint(msg + string.Join(" ", values));
        }
    }
}