Problem:
Score : 600 points

Problem Statement

There is a grid of squares with H+1 horizontal rows and W vertical columns.

You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.

For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print -1 instead.

Constraints

1 \leq H,W \leq 2\times 10^5

1 \leq A_i \leq B_i \leq W

Input

Input is given from Standard Input in the following format:

H W
A_1 B_1
A_2 B_2
:
A_H B_H

Output

Print H lines. The i-th line should contain the answer for the case k=i.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in Rust (1.42.0) (judge verdict: Accepted)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let h: usize = s.next().unwrap().parse().unwrap();
	let w: usize = s.next().unwrap().parse().unwrap();

	let mut mp: std::collections::BTreeSet<_> = (1..=w).map(|i| (i, i)).collect();
	let mut mins = std::collections::BTreeMap::new();
	mins.insert(0, w);

	use std::io::Write;
	let out = std::io::stdout();
	let mut out = out.lock();
	for h in 0..h {
		let l: usize = s.next().unwrap().parse().unwrap();
		let r: usize = s.next().unwrap().parse().unwrap();
		let mut max = None;
		while let Some(p) = mp.range((l, 0)..=(r, std::usize::MAX)).next().cloned() {
			if Some(p.1) > max {
				max = Some(p.1);
			}
			let step = p.0 - p.1;
			if let Some(v) = mins.get_mut(&step) {
				*v -= 1;
			}
			mp.remove(&p);
		}
		match max {
			Some(max) if r + 1 <= w => {
				mp.insert((r + 1, max));
				*mins.entry(r + 1 - max).or_insert(0) += 1;
			}
			_ => (),
		}
		let min = loop {
			if let Some((&k, &v)) = mins.iter().next() {
				if v == 0 {
					mins.remove(&k);
				} else {
					break k as i64;
				}
			} else {
				break -1;
			}
		};
		writeln!(out, "{}", if min < 0 { -1 } else { min + (h + 1) as i64 }).unwrap();
	}
}