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: Wrong Answer)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! flush {
    () => {
        std::io::stdout().flush().unwrap();
    };
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

// @algebra.hyper.rs
// @algebra.group.rs
trait Group:
    std::ops::Add<Output = Self>
    + std::ops::Sub<Output = Self>
    + std::ops::Neg<Output = Self>
    + std::iter::Sum
    + Clone
    + Copy
{
    fn zero() -> Self;
}
impl Group for i32 {
    fn zero() -> Self {
        0
    }
}
impl Group for i64 {
    fn zero() -> Self {
        0
    }
}
impl Group for i128 {
    fn zero() -> Self {
        0
    }
}
impl Group for f32 {
    fn zero() -> Self {
        0.0
    }
}
impl Group for f64 {
    fn zero() -> Self {
        0.0
    }
}

#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Debug)]
enum Hyper<X> {
    NegInf,
    Real(X),
    Inf,
}
use Hyper::{Inf, NegInf, Real};
impl<X> Hyper<X> {
    fn unwrap(self) -> X {
        if let Hyper::Real(x) = self {
            x
        } else {
            panic!()
        }
    }
}
impl<X: Group> std::ops::Add for Hyper<X> {
    type Output = Self;
    fn add(self, rhs: Hyper<X>) -> Hyper<X> {
        match (self, rhs) {
            (Real(x), Real(y)) => Real(x + y),
            (Inf, _) => Inf,
            (_, Inf) => Inf,
            _ => NegInf,
        }
    }
}
impl<X: Group> std::ops::Sub for Hyper<X> {
    type Output = Self;
    fn sub(self, rhs: Hyper<X>) -> Hyper<X> {
        self + (-rhs)
    }
}
impl<X: Group> std::ops::Neg for Hyper<X> {
    type Output = Self;
    fn neg(self) -> Hyper<X> {
        match self {
            Inf => NegInf,
            NegInf => Inf,
            Real(x) => Real(-x),
        }
    }
}

fn search_from(from: usize, w: usize, g: &Vec<(usize, usize)>, ans: &mut Vec<Hyper<i32>>) -> usize {
    let h = g.len();
    let mut u = from;
    for i in 0..h {
        let (a, b) = g[i];
        if u < a || b < u {
            ();
        } else {
            u = b + 1;
            if u >= w {
                return i;
            }
        }
        ans[i] = Real((1 + i + u - from) as i32);
    }
    h
}

fn main() {
    let mut sc = Scanner::new();
    let h: usize = sc.cin();
    let w: usize = sc.cin();
    let g: Vec<(usize, usize)> = (0..h)
        .map(|_| {
            let a = sc.cin::<usize>() - 1;
            let b = sc.cin::<usize>() - 1;
            (a, b)
        })
        .collect();
    let mut ans: Vec<Hyper<i32>> = vec![Inf; h];

    let can = search_from(0, w, &g, &mut ans);
    let _ = search_from(w - 1, w, &g, &mut ans);

    {
        let mut left = 0;
        let mut right = w;
        for _ in 0..200 {
            let mid = (left + right) / 2;
            if search_from(mid, w, &g, &mut ans) < can {
                right = mid;
            } else {
                left = mid;
            }
        }
    }

    for &a in ans.iter() {
        if let Real(x) = a {
            put!(x);
        } else {
            put!(-1);
        }
    }
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}