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, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

// https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 より

macro_rules! eprint {
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = write!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! eprintln {
    () => { eprintln!(""); };
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = writeln!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! dbg {
    ($v:expr) => {{
        let val = $v;
        eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
        val
    }}
}

macro_rules! mat {
    ($($e:expr),*) => { Vec::from(vec![$($e),*]) };
    ($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
    ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
    ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
    ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
        $a$([$i])*.$f($($t),*)
    };
    ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
        let t = $e;
        ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
    } };
}

pub fn readln() -> String {
    let mut line = String::new();
    ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
    line
}

macro_rules! read {
    ($($t:tt),*; $n:expr) => {{
        let stdin = ::std::io::stdin();
        let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
            let line = line.unwrap();
            let mut it = line.split_whitespace();
            _read!(it; $($t),*)
        }).collect::<Vec<_>>();
        ret
    }};
    ($($t:tt),*) => {{
        let line = readln();
        let mut it = line.split_whitespace();
        _read!(it; $($t),*)
    }};
}

macro_rules! _read {
    ($it:ident; [char]) => {
        _read!($it; String).chars().collect::<Vec<_>>()
    };
    ($it:ident; [u8]) => {
        Vec::from(_read!($it; String).into_bytes())
    };
    ($it:ident; usize1) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
    };
    ($it:ident; [usize1]) => {
        $it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
    };
    ($it:ident; [$t:ty]) => {
        $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
    };
    ($it:ident; $t:ty) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
    };
    ($it:ident; $($t:tt),+) => {
        ($(_read!($it; $t)),*)
    };
}


pub fn main() {
    let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

// const MOD: usize = 998244353;
const MOD: usize = 1_000_000_007;
const INF: i64 = std::i64::MAX/2;

// https://yukicoder.me/submissions/379658

pub trait TE {
    type T: Clone;
    type E: Clone;
    fn fold(l: Self::T, r: Self::T) -> Self::T;
    fn eval(p: Self::T, x: Self::E) -> Self::T;
    fn merge(f: Self::E, g: Self::E) -> Self::E;
    fn e() -> Self::T;
    fn id() -> Self::E;
}

pub struct LazySegmentTree<R: TE> {
    size: usize,
    bit: usize,
    a: Vec<(R::T, R::E)>,
}

impl <R: TE> LazySegmentTree<R> {
    pub fn new(n: usize) -> LazySegmentTree<R> {
        let mut bit = 0;
        while (1 << bit) < n {
            bit += 1;
        }
        LazySegmentTree {
            size: 1 << bit,
            bit: bit,
            a: vec![(R::e(), R::id()); 2 << bit],
        }
    }
    pub fn build_by(z: &[R::T]) -> LazySegmentTree<R> {
        let n = z.len();
        let mut bit = 0;
        while (1 << bit) < n {
            bit += 1;
        }
        let mut a = vec![(R::e(), R::id()); 2 << bit];
        for (a, z) in a[(1 << bit)..].iter_mut().zip(z.iter()) {
            a.0 = z.clone();
        }
        for i in (1..(1 << bit)).rev() {
            let l = R::eval(a[2 * i].0.clone(), a[2 * i].1.clone());
            let r = R::eval(a[2 * i + 1].0.clone(), a[2 * i + 1].1.clone());
            a[i].0 = R::fold(l, r);
        }
        LazySegmentTree {
            size: 1 << bit,
            bit : bit,
            a: a,
        }
    }
    fn eval(&self, k: usize) -> R::T {
        R::eval(self.a[k].0.clone(), self.a[k].1.clone())
    }
    fn propagate(&mut self, x: usize) {
        let x = x + self.size;
        for i in (1..(self.bit + 1)).rev() {
            let k = x >> i;
            self.a[2 * k].1 = R::merge(self.a[2 * k].1.clone(), self.a[k].1.clone());
            self.a[2 * k + 1].1 = R::merge(self.a[2 * k + 1].1.clone(), self.a[k].1.clone());
            self.a[k].1 = R::id();
            self.a[k].0 = R::fold(self.eval(2 * k), self.eval(2 * k + 1));
        }
    }
    fn save(&mut self, x: usize) {
        let x = x + self.size;
        for i in 1..(self.bit + 1) {
            let k = x >> i;
            self.a[k].0 = R::fold(self.eval(2 * k), self.eval(2 * k + 1));
        }
    }
    pub fn update(&mut self, l: usize, r: usize, op: R::E) {
        self.propagate(l);
        self.propagate(r - 1);
        let mut x = l + self.size;
        let mut y = r + self.size;
        while x < y {
            if x & 1 == 1 {
                self.a[x].1 = R::merge(self.a[x].1.clone(), op.clone());
                x += 1;
            }
            if y & 1 == 1 {
                y -= 1;
                self.a[y].1 = R::merge(self.a[y].1.clone(), op.clone());
            }
            x >>= 1;
            y >>= 1;
        }
        self.save(l);
        self.save(r - 1);
    }
    pub fn find(&mut self, l: usize, r: usize) -> R::T {
        self.propagate(l);
        self.propagate(r - 1);
        let mut x = l + self.size;
        let mut y = r + self.size;
        let mut p = R::e();
        let mut q = R::e();
        while x < y {
            if x & 1 == 1 {
                p = R::fold(p, self.eval(x));
                x += 1;
            }
            if y & 1 == 1 {
                y -= 1;
                q = R::fold(self.eval(y), q);
            }
            x >>= 1;
            y >>= 1;
        }
        R::fold(p, q)
    }
}

struct R;
impl TE for R {
    type T = (i64,usize);
    type E = (i64,usize);
    fn fold(l: Self::T, r: Self::T) -> Self::T {
        max(l,r)
    }
    fn eval(p: Self::T, x: Self::E) -> Self::T {
        if x.1 > p.1 {
            x
        }
        else {
            p
        }
    }
    fn merge(f: Self::E, g: Self::E) -> Self::E {
        if f.1 > g.1 {
            f
        }
        else {
            g
        }
    }
    fn e() -> Self::T {
        (-INF-1,0)
    }
    fn id() -> Self::E {
        (0,0)
    }
}

struct R2;
impl TE for R2 {
    type T = (i64,usize);
    type E = (i64,usize);
    fn fold(l: Self::T, r: Self::T) -> Self::T {
        min(l,r)
    }
    fn eval(p: Self::T, x: Self::E) -> Self::T {
        if x.1 > p.1 {
            x
        }
        else {
            p
        }
    }
    fn merge(f: Self::E, g: Self::E) -> Self::E {
        if f.1 > g.1 {
            f
        }
        else {
            g
        }
    }
    fn e() -> Self::T {
        (INF,0)
    }
    fn id() -> Self::E {
        (0,0)
    }
}

fn solve() {
    let (h,w) = read!(usize,usize);
    let ab = read!(usize,usize;h);
    let mut seg_max = LazySegmentTree::<R>::new(w);
    let mut seg_min = LazySegmentTree::<R2>::new(w);
    let mut idx = 1;
    for i in 0..w {
        seg_max.update(i,i+1,(i as i64, idx));
        seg_min.update(i,i+1,(0 as i64, idx));
        idx += 1;
    }
    for (i, &(a,b)) in ab.iter().enumerate() {
        let s = a-1;
        let t = b-1;
        let dst = t;
        let (val,_) = seg_max.find(s,t+1);
        seg_max.update(s,t+1,(-INF,idx));
        seg_min.update(s,t+1,(INF,idx));
        idx += 1;
        if t!=w-1 {
            let maval = max(seg_max.find(t+1,t+2).0,val);
            seg_max.update(t+1,t+2,(maval,idx));
            let mival = min(seg_min.find(t+1,t+2).0,(t+1) as i64-val);
            seg_min.update(t+1,t+2,(mival,idx));
        }
        idx += 1;
        // for j in 0..w {
        //     print!("{} ", seg_max.find(j,j+1).0);
        // }
        // println!();
        // for j in 0..w {
        //     print!("{} ", seg_min.find(j,j+1).0);
        // }
        // println!();
        let ans = seg_min.find(0,w).0+i as i64+1;
        if ans < INF {
            println!("{}",ans);
        }
        else {
            println!("-1");
        }
    }
}

fn run() {
    solve();
}