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.PrintWriter;
import java.util.*;


public class Main {
    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        Task task = new Task();
        task.solve(sc, out);
        out.flush();
        sc.close();
    }

    static class Task {
        public void solve(Scanner sc, PrintWriter out){
            int n = nint(sc);
            long t = nlong(sc);
            List<Long> tList = getLongList(sc, n);
            long count = 0;
            long before = 0;
            for (int i = 0; i < n; i++) {
                long x = tList.get(i);
                long margin = x - before;
                if (margin <= t){
                    count += margin;
                }else{
                    count += t;
                }
                before = x;
            }
            count += t;
            out.println(count);

        }
    }


    static int nint(Scanner sc) {
        return Integer.parseInt(sc.next());
    }

    static long nlong(Scanner sc) {
        return Long.parseLong(sc.next());
    }

    static double ndouble(Scanner sc) {
        return Double.parseDouble(sc.next());
    }

    static float nfloat(Scanner sc) {
        return Float.parseFloat(sc.next());
    }

    static String nstr(Scanner sc) {
        return sc.next();
    }

    static long[] longLine(Scanner sc, int size) {
        long[] lLine = new long[size];
        for (int i = 0; i < size; i++) {
            lLine[i] = nlong(sc);
        }
        return lLine;
    }

    static int[] intLine(Scanner sc, int size) {
        int[] iLine = new int[size];
        for (int i = 0; i < size; i++) {
            iLine[i] = nint(sc);
        }
        return iLine;
    }

    static String[] strLine(Scanner sc, int size) {
        String[] strLine = new String[size];
        for (int i = 0; i < size; i++) {
            strLine[i] = nstr(sc);
        }
        return strLine;
    }

    static long maxFromList(List<Long> longList) {
        return longList.stream().max(Comparator.naturalOrder()).get();
    }

    static long minFromList(List<Long> longList) {
        return longList.stream().min(Comparator.naturalOrder()).get();
    }

    public static int sumDigits(int n) {
        int sum = 0;
        while (n != 0) {
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }

    public static long sumDigits(long n) {
        long sum = 0;
        while (n != 0) {
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }

    static List<Integer> getIntegerList(Scanner sc, int size) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            list.add(nint(sc));
        }
        return list;
    }

    static List<Long> getLongList(Scanner sc, int size) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            list.add(nlong(sc));
        }
        return list;
    }

    static List<String> getStringList(Scanner sc, int size){
        List<String> stringList = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            stringList.add(nstr(sc));
        }
        return stringList;
    }

    private static long lcm(long a, long b) {
        return a * b / gcd(b, a % b);
    }

    private static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }
    private static Map<Integer, Integer> primeFactorize(long num) {
        Map<Integer, Integer> map = new HashMap<>();
        int i = 2;
        while (i * i <= num) {
            while (num % i == 0) {
                num /= i;
                if (map.containsKey(i)) {
                    int tmp = map.get(i);
                    tmp++;
                    map.put(i, tmp);
                } else {
                    map.put(i, 1);
                }
            }
            i ++;
        }
        if (num > 1)
            map.put((int) num, 1);
        return map;
    }
}