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.Text;
using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        Solver sol = new Solver();
        sol.Solve();
    }
}

class Solver
{
    int N;
    int T;
    int[] t;
    int X;

    public void Solve()
    {
        X = T;
        for(int i = 1; i <= N - 1; i++)
        {
            if (t[i - 1] + T < t[i])
            {
                X += T;
            }
            else
            {
                X += t[i] - t[i - 1];
            }
        }
        Console.WriteLine(X);
    }

    public Solver()
    {
        int[] nt = ReadIntArray();
        t = ReadIntArray();
        N = nt[0];
        T = nt[1];
    }

    static String ReadString() { return Console.ReadLine(); }
    static int ReadInt() { return int.Parse(Console.ReadLine()); }
    static long ReadLong() { return long.Parse(Console.ReadLine()); }
    static double ReadDouble() { return double.Parse(Console.ReadLine()); }
    static String[] ReadStringArray() { return Console.ReadLine().Split(' '); }
    static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToArray(); }
    static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(e => long.Parse(e)).ToArray(); }
    static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(e => double.Parse(e)).ToArray(); }
}