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)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;
use std::ops::Bound::*;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<usize>();
    let (h, w) = (v[0], v[1]);
    let mut spans = vec![];
    for i in 0..h {
        let v = read_vec::<usize>();
        let (a, b) = (v[0] - 1, v[1] - 1);
        spans.push((a, b));
    }

    let mut to = BTreeMap::new();
    let mut costs = MultiSet::new();
    for x in 0..w {
        to.insert(x, 0);
        costs.insert(0);
    }

    for (i, (l, r)) in spans.into_iter().enumerate() {
        let mut ins = to.range((Included(l), Included(r)));
        let mut dels = vec![];

        while let Some(x) = ins.next() {
            dels.push((*x.0, *x.1));
            costs.remove(x.1);
        }

        if !dels.is_empty() {
            for x in &dels {
                to.remove(&x.0);
            }
            if r != w - 1 {
                let (last_x, last_cost) = dels[dels.len() - 1];
                let next_cost = r + 1 - last_x + last_cost;
                if !to.contains_key(&(r + 1)) || next_cost < to[&(r + 1)] {
                    to.insert(r + 1, next_cost);
                    costs.insert(next_cost);
                }
            }
        }

        if let Some(x) = costs.map.iter().next() {
            println!("{}", *x.0 + 1 + i);
        } else {
            println!("-1");
        }
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

struct MultiSet<T> {
    size: usize,
    map: std::collections::BTreeMap<T, u32>,
}

impl<T> MultiSet<T>
where
    T: Ord,
{
    fn new() -> Self {
        MultiSet {
            size: 0,
            map: std::collections::BTreeMap::new(),
        }
    }
    fn len(&self) -> usize {
        self.map.len()
    }
    fn insert(&mut self, val: T) {
        self.size += 1;
        *self.map.entry(val).or_insert(0) += 1;
    }
    fn remove(&mut self, val: &T) {
        assert!(self.map.contains_key(val));
        let cnt = self.map.get_mut(val).unwrap();
        *cnt -= 1;
        if *cnt == 0 {
            self.map.remove(val);
        }
    }
}