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.util.*;

public class Main {
	public static void main(String[] args) {
		int N = NI();
		int T = NI();
		long t[] = new long[N+1];
		for (int i = 0; i < N; i++) {
			t[i] = NI();
		}
		t[N] = 1L << 45;
		long ans = 0;
		long st = t[0];
		for (int i = 1; i <= N; i++) {
			if (t[i-1] + T < t[i]) {
				ans += T + t[i - 1] - st;
				st = t[i];
			}
		}
		System.out.println(ans);
	}

	static int NI() {
		try {
			int c = System.in.read(), r = 0;
			for (; c != '-' && (c < '0' || '9' < c);) {
				c = System.in.read();
			}
			if (c == '-')
				return -NI();
			for (; '0' <= c && c <= '9'; c = System.in.read()) {
				r = r * 10 + c - '0';
			}
			return r;
		} catch (Exception e) {
			return -1;
		}
	}

	static String next() {
		try {
			StringBuilder res = new StringBuilder("");
			int c = System.in.read();
			while (Character.isWhitespace(c))
				c = System.in.read();
			do {
				res.append((char) c);
			} while (!Character.isWhitespace(c = System.in.read()));
			return res.toString();
		} catch (Exception e) {
			return null;
		}
	}
}