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;
use std::cmp;

fn main() {
    let mut line = String::new();
    io::stdin().read_line(&mut line);
    let mut line = line.split_whitespace();
    let n = line.next().unwrap().parse::<i64>().unwrap();
    let t = line.next().unwrap().parse::<i64>().unwrap();
    
    let mut a = [0i64; 200_000];
    let mut line = String::new();
    io::stdin().read_line(&mut line);
    let mut line = line.split_whitespace();
    for i in 0..n {
        let l = line.next();
        let ll = l.unwrap();
        let lll = ll.parse::<i64>();
        a[i as usize] = lll.unwrap();
    }

    let mut delta = [0i64; 199_999];
    for i in 0..(n-1) {
        delta[i as usize] = cmp::max(0i64, a[i as usize + 1usize] - a[i as usize] - t);
    }
    let mut x = a[n as usize - 1usize] + t;
    
    for i in 0..(n-1) {
        x -= delta[i as usize];
    }

    println!("{}", x);
}