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;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

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

    let mut start = BTreeMap::new();
    let mut moves = BTreeSet::new();
    for j in 0..w {
        start.insert(j, j);
        moves.insert((0, j));
    }
    for i in 0..h {
        let (ai, bi) = ab[i];
        let mut keys = vec![];
        for (&k, _) in start.range(ai..=bi) {
            keys.push(k);
        }
        if !start.contains_key(&(bi + 1)) && !keys.is_empty() && bi + 1 < w {
            start.insert(bi + 1, start[&keys[keys.len() - 1]]);
            moves.insert((bi - start[&(bi + 1)] + 1, bi + 1));
        }
        for &k in &keys {
            let v = start[&k];
            start.remove(&k);
            moves.remove(&(k - v, k));
        }
        // eprintln!("{:?}", start);
        // eprintln!("{:?}", moves);
        if let Some((d, _)) = moves.range(..).nth(0) {
            println!("{}", i + d + 1);
        } else {
            println!("-1");
        }
    }
}