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)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

use std::collections::{BTreeSet, BinaryHeap};
const INF: usize = 999999999999;

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

    let mut s = BTreeSet::new();
    let mut heap = BinaryHeap::new();
    for i in 1..=w {
        s.insert((i, 0));
        heap.push((0_isize, i));
    }
    for k in 1..=h {
        input! {
            a:usize,b:usize,
        }
        if b == w {
            let r = s
                .range((a, 0)..=(b, INF))
                .map(|q| *q)
                .collect::<BTreeSet<_>>();
            s = &s - &r;
        } else {
            let mut r = s.range((a, 0)..=(b, INF));
            let (mut idx, mut value) = (INF, INF);
            if let Some(x) = r.next_back() {
                idx = x.0;
                value = x.1;
            }
            if idx != INF {
                let del = s
                    .range((b + 1, 0)..=(b + 1, INF))
                    .map(|q| *q)
                    .collect::<BTreeSet<_>>();
                if del.len() == 0 {
                    s.insert((b + 1, b + 1 - idx + value));
                    heap.push((-1 * (b + 1 - idx + value) as isize, b + 1));
                    let r = s
                        .range((a, 0)..=(b, INF))
                        .map(|q| *q)
                        .collect::<BTreeSet<_>>();
                    s = &s - &r;
                } else {
                    s = &s - &del;
                }
            }
        }
        //dbg!(&s);
        while !heap.is_empty() {
            let p = heap.peek().unwrap();
            let idx = p.1;
            let value = (p.0 * -1) as usize;
            if !s.contains(&(idx, value)) {
                heap.pop();
            } else {
                break;
            }
        }
        if heap.is_empty() {
            println!("-1");
        } else {
            println!("{}", k + (heap.peek().unwrap().0 * -1) as usize);
        }
    }
}