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;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - Sentou
            var line = ReadLine().ToList();
            int n = line[0];    //スイッチの押された回数
            int t = line[1];    //お湯の出続ける秒数

            long totalTime = CalcTotalTimeOfHotWater(n, t);
            Console.WriteLine(totalTime);
        }

        static long CalcTotalTimeOfHotWater(int n, int t)
        {
            var people = ReadLine().ToList();

            int startTime = 0;
            int endTime = t;
            long sum = 0;

            for(int i = 1; i < n; i++)
            {
                int nextStartTime = people[i];

                if (nextStartTime < endTime)
                {
                    int diff = nextStartTime - startTime;
                    sum += diff;
                }
                else
                {
                    sum += t;
                }

                startTime = nextStartTime;
                endTime = startTime + t;
            }

            return sum + t;
        }

        static IEnumerable<int> ReadLine()
        {
            var line = Console.ReadLine().TrimEnd();
            var array = line.Split(' ');

            foreach (var s in array)
            {
                yield return int.Parse(s);
            }
        }
    }
}