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::{BufRead, Write};
use std::io;
use std::cmp;

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let mut split = s.split_whitespace();
    let n = split.next().unwrap().parse::<i64>().unwrap();
    let t = split.next().unwrap().parse::<i64>().unwrap();
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let ts = s.split_whitespace()
        .map(|s| s.parse::<i64>().unwrap())
        .collect::<Vec<_>>();
    let mut sum = t;
    for i in 1..ts.len() {
        sum += cmp::min(ts[i] - ts[i - 1], t);
    }
    writeln!(output, "{}", sum).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("2 4
0 3\n",
             "7\n");
    }
    #[test]
    fn case2() {
        test("2 4
0 5\n",
             "8\n");
    }
    #[test]
    fn case3() {
        test("4 1000000000
0 1000 1000000 1000000000\n",
             "2000000000\n");
    }
    #[test]
    fn case4() {
        test("1 1
0\n",
             "1\n");
    }
    #[test]
    fn case5() {
        test("9 10
0 3 5 7 100 110 200 300 311\n",
             "67\n");
    }
}