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: Accepted)



import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] tmpArray = br.readLine().split(" ");

		int n = Integer.parseInt(tmpArray[0]);
		int t = Integer.parseInt(tmpArray[1]);

		int input[] = new int[n];

		tmpArray = br.readLine().split(" ");

		for(int i = 0; i < n; i++){
			input[i] = Integer.parseInt(tmpArray[i]);
		}

		if(n == 1){
			System.out.println(t);
			return;
		}
		int start = 0;

		long total = 0;
		for(int i = 1; i < n; i++){
			if(input[i] - input[i - 1] > t){
				total += input[i - 1] + t - input[start];
				start = i;
			}

			if(i == n - 1) {
				if(start == n - 1){
					total += t;
				}
				else {
					total += input[i] + t - input[start];
				}
			}

		}

		System.out.println(total);
	}

}