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;

namespace ABC060_C_Sentou
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			string[] input = Console.ReadLine().Split(' ');
			int n = int.Parse(input[0]);
			long t = long.Parse(input[1]);
			input = Console.ReadLine().Split(' ');
			List<long> tList = new List<long>(n);
			for(int i = 0; i < n; i++)
				tList.Add(long.Parse(input[i]));

			long time = 0;
			int timeStartIndex = 0; //このインデックスからお湯が出続けている
			for (int i = 0; i < n - 1; i++)
			{
				//この場合途中でお湯が止まっている
				if (tList[i + 1] - tList[i] > t)
				{
					time += tList[i] - tList[timeStartIndex] + t;
					timeStartIndex = i + 1;
				}
			}
			time += tList[n - 1] - tList[timeStartIndex] + t;
			
			Console.WriteLine(time);
		}
	}
}