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: Time Limit Exceeded)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{input, marker::*, fastout};
use superslice::*;

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

    let mut range = BTreeSet::new();
    let mut dists = BTreeMap::new();
    for i in 0..w {
        range.insert((i, i)); // (end, start)
    }
    dists.insert(0, w);

    for k in 0..h {
        let (a, b) = ab[k];
        let cloned = range.clone();
        let mut last_end = 1<<60;
        for &(end, start) in cloned.iter().rev() {
            if a <= end && end <= b {
                range.remove(&(end, start));
                let entry = dists.get_mut(&(end - start)).unwrap();
                if *entry == 1 {
                    dists.remove(&(end - start));
                } else {
                    *entry -= 1;
                }
                let end = if b == w - 1 { 1<<60 } else { b + 1 };
                if end != last_end {
                    last_end = end;
                    range.insert((end, start));
                    *dists.entry(end - start).or_insert(0) += 1;
                }
            } else {
                last_end = end;
            }
        }
        let res = *dists.iter().next().unwrap_or((&(1<<60), &0)).0;
        if res >= w {
            println!("-1");
        } else {
            println!("{}", res + k + 1);
        }
    }
}