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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
 
namespace AtCoder
{
    class AC073C
    {
#if true
        static void Main(string[] args)
        {
            string s1 = Console.ReadLine();
            string s2 = Console.ReadLine();
 
            Console.WriteLine(funcMain(s1,s2));
#if DEBUG
            Console.ReadKey();
#endif
        }
 
#else
        static void Main(string[] args)
        {
            test();
        }
#endif
 
        static private string funcMain(string arg1, string arg2)
        {
            string[] bufarray;
            bufarray = arg1.Split();
            int Ninzu = int.Parse(bufarray[0]);
            long OneTime = long.Parse(bufarray[1]);
            long TotalTime = 0;
            long NowTime = 0;
 
            foreach (string buf in arg2.Split())
            {
                long t = long.Parse(buf);
 
                if (t == 0) continue;
 
                if (t > OneTime)
                {
                    TotalTime += OneTime;
                }
                else
                {
                    TotalTime += t - NowTime;
                }
                NowTime = t;
            }
 
            TotalTime += OneTime;
 
            return TotalTime.ToString();
        }
 
        static private void test()
        {
            string arg1, arg2;
            arg1 = "2 4";
            arg2 = "0 3";
            Console.WriteLine("7" == funcMain(arg1, arg2));
            arg1 = "2 4";
            arg2 = "0 5";
            Console.WriteLine("8" == funcMain(arg1, arg2));
            arg1 = "4 1000000000";
            arg2 = "0 1000 1000000 1000000000";
            Console.WriteLine("2000000000" == funcMain(arg1, arg2));
            arg1 = "1 1";
            arg2 = "0";
            Console.WriteLine("1" == funcMain(arg1, arg2));
            arg1 = "9 10";
            arg2 = "0 3 5 7 100 110 200 300 311";
            Console.WriteLine("67" == funcMain(arg1, arg2));
            Console.ReadKey();
        }
 
    }
}