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;

namespace AtCoder
{
    class Program
    {
        static IO io = new IO();

        static void Main(string[] args)
        {
            io.ReadSplit();
            int N = io.Int();
            long T = io.Long();
            io.ReadSplit();
            long[] t = io.Long(N);

            io.WriteLine(Calc(N, T, t).ToString());
        }

        private static long Calc(int N, long T, long[] t)
        {
            long total = 0;
            int start = 0;
            int i = 0;
            while (i < N - 1)
            {
                if (t[i] + T < t[i + 1])
                {
                    total += t[i] + T - t[start];
                    start = i + 1;
                }
                i += 1;
            }
            total += t[N - 1] + T - t[start];
            return total;
        }
    }
    class IO
    {
        private string[] _Inputs;
        private int _Index;
        public void Read()
        {
            _Inputs = new string[1];
            _Inputs[0] = Console.ReadLine();
            _Index = 0;
        }
        public void ReadSplit()
        {
            _Inputs = Console.ReadLine().Split(' ');
            _Index = 0;
        }
        public string String()
        {
            return _Inputs[_Index++];
        }
        public string[] String(int xCount)
        {
            string[] rv = new string[xCount];
            Array.Copy(_Inputs, _Index, rv, 0, xCount);
            _Index += xCount;
            return rv;
        }
        public int Int()
        {
            return int.Parse(_Inputs[_Index++]);
        }
        public int[] Int(int xCount)
        {
            int[] rv = new int[xCount];
            for (int i = 0; i < xCount; ++i)
            {
                rv[i] = int.Parse(_Inputs[_Index++]);
            }
            return rv;
        }
        public long Long()
        {
            return long.Parse(_Inputs[_Index++]);
        }
        public long[] Long(int xCount)
        {
            long[] rv = new long[xCount];
            for (int i = 0; i < xCount; ++i)
            {
                rv[i] = long.Parse(_Inputs[_Index++]);
            }
            return rv;
        }
        public void Write(string xStr)
        {
            Console.Write(xStr);
        }
        public void WriteLine(string xStr)
        {
            Console.WriteLine(xStr);
        }
    }
}