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::*},
    std::cmp::*,
    std::collections::*,
    std::ops::*,
};

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

    let mut s = BTreeSet::<(usize, usize)>::new();
    let mut v = BTreeSet::<(usize, usize)>::new();
    for i in 0..w {
        s.insert((i, i));
        v.insert((0, i));
    }

    for (i, &(a, b)) in ab.iter().enumerate() {
        let mut next = s.clone();
        let mut update = None;
        for &(end, start) in s.range((a, 0)..(b, w)) {
            next.remove(&(end, start));
            v.remove(&(end - start, start));
            update = Some(start);
        }
        if b + 1 != w {
            if let Some(start) = update {
                next.insert((b + 1, start));
                v.insert((b + 1 - start, start));
            }
        }
        if v.is_empty() {
            println!("{}", -1);
        } else {
            println!("{}", 1 + i + v.iter().next().unwrap().0);
        }
        s = next;
    }
}