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-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static System.Array;

class Program
{
    public static void Main()
    {
        var n = ReadLine().Split().Select(long.Parse).ToArray();
        var a = ReadLine().Split().Select(long.Parse).ToArray();
        var t = new Tuple<long, long>[n[0]];
        for(int i = 0; i < n[0]; i++)
        {
            t[i] = new Tuple<long, long>(a[i], a[i] + n[1]);
        }
        var sum = 0L;
        for(int i = 0; i < n[0] - 1; i++)
        {
            if(t[i].Item2 > t[i + 1].Item1)
                t[i] = new Tuple<long, long>(t[i].Item1, t[i + 1].Item1);
        }
        for(int i = 0; i < n[0]; i++)
        {
            sum += t[i].Item2 - t[i].Item1;
        }
        WriteLine(sum);
    }
}