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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.*;
import java.lang.reflect.Array;
import java.nio.channels.ScatteringByteChannel;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
 
public class Main {
    public static void main (String[] args) throws IOException
    {
    	  Scanner sc = new Scanner(System.in);
    	  int N = sc.nextInt();
    	  int T = sc.nextInt();
    	  int t[] = new int [100000004 + T];
    	  int c[] = new int [100000004 + T];
    	  int d[] = new int [100000004 + T];
    	  long ans = 1;
    	  
    	  for (int i = 0 ; i<=N+4 ; i++){
    		 c[i] = 0;
    	  }
    	  
    	  for (int i = 1 ; i<=N ; i++){
    		  t[i] = sc.nextInt();
    		  c[t[i]] = c[t[i]] + 1;
    		  c[t[i] + T] = c[t[i] + T] - 1;
    	  }
    	  
    	  d[0] = 1;
    	  for (int i = 1 ; i<= t[N] + T + 2 ; i++){
    		  d[i] = d[i-1] + c[i];
    		  if (d[i] > 0) {
    			  ans = ans + 1;
    		  }
    		  
    	  }
    	  
    	  System.out.println(ans);
    }
    
}