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)

use std::io::Read;
use std::cmp::min;
use im_rc::HashSet;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let h: usize = iterator.next().unwrap().parse().unwrap();
    let w: usize = iterator.next().unwrap().parse().unwrap();
    let bars: Vec<(usize, usize)> =
        (0..h)
            .map(|_| {
                let ai: usize = iterator.next().unwrap().parse().unwrap();
                let bi: usize = iterator.next().unwrap().parse().unwrap();
                (ai - 1, bi - 1)
            })
            .collect();

    let mut ans: Vec<Option<usize>> = vec![None; h + 1];

    let mut visited: HashSet<(usize, usize)> = HashSet::new();
    for j in (0..w).rev() {
        let mut m: usize = 0;
        let mut ci = 0;
        let mut cj = j;
        while ci < h {
            if visited.contains(&(ci, cj)) {
                break;
            }
            visited.insert((ci, cj));
            let bar = bars[ci];
            if cj >= bar.0 && cj <= bar.1 {
                m += bar.1 + 1 - cj;
                cj = bar.1 + 1;
            }
            if cj >= w {
                break;
            }
            ci += 1;
            m += 1;
            if let Some(x) = ans[ci] {
                ans[ci] = Some(min(x, m));
            } else {
                ans[ci] = Some(m);
            }
        }
    }

    let mut result = String::new();
    for i in 1..(h + 1) {
        if let Some(x) = ans[i] {
            result.push_str(&format!("{}\n", x));
        } else {
            result.push_str("-1\n");
        }
    }
    result.trim().to_string()
}