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)

use {
    proconio::{input, marker::Usize1},
    std::{
        collections::{BTreeSet, BTreeMap},
        ops::Bound::Included,
    },
};

const M: usize = usize::max_value();

fn main() {
    input! {
        h: usize,
        w: usize,
        ab: [(Usize1, Usize1); h],
    }

    let mut es = BTreeSet::new();
    let mut dc = BTreeMap::new();
    for j in 0..w {
        es.insert((j, j));
    }
    dc.insert(0, w);

    for i in 0..h {
        let (a, b) = ab[i];
        let mut rm = vec![];
        let mut add = None;
        for &(e, s) in es.range((Included(&(a, 0)), Included(&(b, w)))).rev() {
            rm.push((e, s));
            if add.is_none() {
                let e = if b == w - 1 { M } else { b + 1 };
                add = Some((e, s));
            }
        }

        for (e, s) in rm {
            es.remove(&(e, s));

            let d = e - s;
            let v = dc.get_mut(&d).unwrap();
            if *v <= 1 {
                dc.remove(&d);
            } else {
                *v -= 1;
            }
        }

        if let Some((e, s)) = add {
            es.insert((e, s));
            *dc.entry(e - s).or_insert(0) += 1;
        }

        let d = if let Some(f) = dc.iter().next() { *f.0 } else { M };
        if d >= w {
            println!("-1");
        } else {
            println!("{}", d + i + 1);
        }
    }
}