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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::prelude::*;
use std::{io};
use std::collections::{HashMap, HashSet, VecDeque};
use std::cmp::Ordering;

fn string_to_nums(s: String) -> Vec<isize> {
    let mut v = Vec::new();
    for part in s.split_whitespace() {
        v.push(part.parse::<isize>().unwrap())
    }
    v
}

fn read_a_line() -> String {
    let mut s = String::new();
    assert!(io::stdin().read_line(&mut s).is_ok());
    s.trim().to_string()
}

fn read_nums() -> Vec<isize> {
    string_to_nums(read_a_line())
}

fn read_next(bytes: &mut io::Bytes<io::Stdin>) -> u64 {
    let mut n = 0;
    while let Some(b) = bytes.next() {
        let b = b.unwrap();
        if b == 32 || b == 10 { return n; }
        n = n * 10 + (b - 48) as u64;
    }
    return n;
}

fn main() {
    let t = read_nums();
    let n = t[0] as u64;
    let t = t[1] as u64;

    let mut bytes = io::stdin().bytes();
    let mut total = 0u64;
    let mut last = read_next(&mut bytes);
    for _ in 1..n {
        let ti = read_next(&mut bytes);
        if ti - last < t {
            total += ti - last
        }
        else {
            total += t
        }
        last = ti;
    }
    total += t;
    println!("{}", total);
}