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)

#[allow(unused_imports)]
use {
    proconio::{fastout, input, marker::*},
    std::cmp::*,
    std::collections::*,
    std::ops::*,
};

#[allow(unused_macros)]
macro_rules !max {($a :expr $(,) *) =>{{$a } } ;($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::max ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::max ($a ,max !($($rest ) ,+) ) } } ;}
#[allow(unused_macros)]
macro_rules !chmax {($base :expr ,$($cmps :expr ) ,+$(,) *) =>{{let cmp_max =max !($($cmps ) ,+) ;if $base <cmp_max {$base =cmp_max ;true } else {false } } } ;}

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

    let mut s = (0..w).map(|i| (i, i)).collect::<BTreeSet<(usize, usize)>>();
    let mut v = (0..w).map(|i| (0, i)).collect::<BTreeSet<(usize, usize)>>();

    for (i, &(a, b)) in ab.iter().enumerate() {
        let update = s
            .range((a, 0)..(b, w))
            .map(|&(i, j)| (i, j))
            .collect::<Vec<(usize, usize)>>(); // total: O(w)log w
        if !update.is_empty() {
            let mut x = 0;
            for (end, start) in update {
                chmax!(x, start);
                s.remove(&(end, start));
                v.remove(&(end - start, start));
            }
            if b != w {
                s.insert((b, x));
                v.insert((b - x, x));
            }
        }
        if let Some((m, _)) = v.iter().next() {
            println!("{}", m + i + 1);
        } else {
            println!("-1");
        }
    }
}