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)

// https://atcoder.jp/contests/abc177/tasks/abc177_f
//
#![allow(unused_imports)]
use std::io::*;
use std::io::Write;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

// Input macros.
// Original by tanakh: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, switch) => {
        {
            let ty = read_value!($iter, i32);
            if ty == 1 {
                vec![ty, read_value!($iter, i32), read_value!($iter, i32)]
            } else if ty == 2 {
                vec![ty, read_value!($iter, i32)]
            } else {
                vec![ty, read_value!($iter, i32)]
            }
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! read_line {
    ($t:tt) => {
        {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            s.trim_right().parse::<$t>().unwrap()
        }
    }
}

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ===

// ====

#[derive(Debug, Clone)]
struct Treap<T> {
    root: Link<T>
}

impl<T: Ord + Copy + Debug> Treap<T> {
    fn new() -> Self {
        Treap {
            root: None
        }
    }

    fn push(&mut self, v: T) -> bool {
        if self.contains(v) {
            return false;
        }
        let u = self.root.take();
        self.root = Node::push(u, v);
        true
    }

    fn remove(&mut self, v: T) -> bool {
        Node::remove(&mut self.root, v)
    }

    fn len(&self) -> usize {
        Node::sz(&self.root)
    }

    fn min(&self) -> Option<T> {
        Node::min(&self.root)
    }

    fn max(&self) -> Option<T> {
        Node::max(&self.root)
    }

    //
    // Returns k-th value in the tree (1-indexed).
    //
    fn kth(&mut self, k: usize) -> Option<T> {
        if k == 0 || Node::sz(&self.root) < k {
            None
        } else {
            let (nl, nr) = Node::split_at(self.root.take(), k-1);
            let val = Node::min(&nr);
            self.root = Node::merge(nl, nr);
            val
        }
    }

    fn contains(&self, value: T) -> bool {
        Node::contains(&self.root, value)
    }

    fn peek_less(&self, value: T) -> Option<T> {
        Node::peek_less(&self.root, value)
    }

    fn count_less(&self, value: T) -> usize {
        Node::count_less(&self.root, value)
    }

    fn peek_greater(&self, value: T) -> Option<T> {
        Node::peek_greater(&self.root, value)
    }
}

struct XorShift {
    x: i64,
    y: i64,
    z: i64,
    w: i64
}

impl XorShift {
    fn rotate(&mut self) {
        let t = self.x ^ (self.x << 11);
        self.x = self.y;
        self.y = self.z;
        self.z = self.w;
        self.w = (self.w ^ (self.w >> 19)) ^ (t ^ (t >> 8));
    }

    fn next_i64(&mut self) -> i64 {
        self.rotate();
        self.w
    }
}

static mut RAND: XorShift = XorShift {
    x: 123456789i64,
    y: 362436069i64,
    z: 521288629i64,
    w: 88675123i64
};

fn generate_next() -> i64 {
    let x;
    unsafe {
        x = RAND.next_i64();
    }
    x
}

type Link<T> = Option<Box<Node<T>>>;

#[derive(Debug, Clone)]
struct Node<T> {
    value: T,
    size: usize,
    priority: i64,
    left: Link<T>,
    right: Link<T>,
}

impl<T: Ord + Copy + Debug> Node<T> {
    fn new(value: T) -> Self {
        Node {
            value: value,
            size: 1,
            priority: generate_next(),
            left: None,
            right: None
        }
    }

    fn sz(node: &Link<T>) -> usize {
        match node.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => 0,
            Some(x) => x.size
        }
    }

    fn calc(node: &mut Link<T>) {
        if let Some(x) = node.as_mut() { // TODO: Remove as_mut() after upgrading above 1.26
            x.size = 1 + Node::sz(&x.left) + Node::sz(&x.right);
        }
    }

    fn merge(left: Link<T>, right: Link<T>) -> Link<T> {
        match (left, right) {
            (None, None) => None,
            (None, x) => x,
            (x, None) => x,
            (Some(l), Some(r)) => {
                if l.priority < r.priority {
                    let mut l = l;
                    l.right = Self::merge(l.right.take(), Some(r));
                    let mut l = Some(l);
                    Node::calc(&mut l);
                    l
                } else {
                    let mut r = r;
                    r.left = Self::merge(Some(l), r.left.take());
                    let mut r = Some(r);
                    Node::calc(&mut r);
                    r
                }
            }
        }
    }

    fn min(now: &Link<T>) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None    => None,
            Some(x) => {
                match x.left.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
                    None    => Some(x.value),
                    Some(_) => Self::min(&x.left)
                }
            }
        }
    }

    fn max(now: &Link<T>) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None    => None,
            Some(x) => {
                match x.right.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
                    None    => Some(x.value),
                    Some(_) => Self::max(&x.right)
                }
            }
        }
    }

    fn contains(now: &Link<T>, value: T) -> bool {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => false,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less    => Self::contains(&x.left, value),
                    Ordering::Equal   => true,
                    Ordering::Greater => Self::contains(&x.right, value)
                }
            }
        }
    }

    fn count_less(now: &Link<T>, value: T) -> usize {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => 0,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less | Ordering::Equal => {
                        Self::count_less(&x.left, value)
                    },
                    Ordering::Greater => {
                        let w = Self::count_less(&x.right, value);
                        Node::sz(&x.left) + 1 + w
                    }
                }
            }
        }
    }

    fn peek_less(now: &Link<T>, value: T) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => None,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less | Ordering::Equal => {
                        Self::peek_less(&x.left, value)
                    },
                    Ordering::Greater => {
                        let w = Self::peek_less(&x.right, value);
                        if w == None {
                            Some(x.value)
                        } else {
                            Some(max(w.unwrap(), x.value))
                        }
                    }
                }
            }
        }
    }

    fn peek_greater(now: &Link<T>, value: T) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => None,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Greater | Ordering::Equal => {
                        Self::peek_greater(&x.right, value)
                    },
                    Ordering::Less => {
                        let w = Self::peek_greater(&x.left, value);
                        if w == None {
                            Some(x.value)
                        } else {
                            Some(min(w.unwrap(), x.value))
                        }
                    }
                }
            }
        }
    }

    fn split_at(now: Link<T>, k: usize) -> (Link<T>, Link<T>) {
        match now {
            None => (None, None),
            Some(x) => {
                let mut x = x;
                let lsz = Self::sz(&x.left);
                if k <= lsz {
                    let (nl, nr) = Self::split_at(x.left.take(), k);
                    x.left = nr;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (nl, x)
                } else {
                    let (nl, nr) = Self::split_at(x.right.take(), k-1-lsz);
                    x.right = nl;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (x, nr)
                }
            },
        }
    }

    fn split_by(now: Link<T>, v: T) -> (Link<T>, Link<T>) {
        match now {
            None => (None, None),
            Some(x) => {
                let mut x = x;
                if v <= x.value {
                    let (nl, nr) = Self::split_by(x.left.take(), v);
                    x.left = nr;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (nl, x)
                } else {
                    let (nl, nr) = Self::split_by(x.right.take(), v);
                    x.right = nl;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (x, nr)
                }
            },
        }
    }

    fn push(now: Link<T>, new_value: T) -> Link<T> {
        let new_node = Some(Box::new(Node::new(new_value)));
        let (left, right) = Self::split_by(now, new_value);
        Self::merge(Self::merge(left, new_node), right)
    }

    fn remove(now: &mut Link<T>, target_value: T) -> bool {
        let mut both_none = false;
        let w = match now.as_mut() { // TODO: Remove as_mut() after upgrading above 1.26
            None => false,
            Some(x) => {
                if target_value < x.value {
                    Self::remove(&mut x.left, target_value)
                } else if x.value < target_value {
                    Self::remove(&mut x.right, target_value)
                } else {
                    let new_link = Self::merge(x.left.take(), x.right.take());
                    if let Some(node) = new_link {
                        *x = node;
                    } else {
                        both_none = true;
                    }
                    true
                }
            }
        };
        Node::calc(now);
        if both_none {
            now.take();
        }
        w
    }
}

// ====

const INF: usize = 1e12 as usize;

struct PositionSet {
    position_value_set: Treap<(usize, usize, usize)>,
    value_position_set: Treap<(usize, usize, usize)>
}

impl PositionSet {
    fn new() -> Self {
        Self {
            position_value_set: Treap::new(),
            value_position_set: Treap::new()
        }
    }

    fn push(&mut self, position: usize, value: usize, d: usize) {
        self.position_value_set.push((position, value, d));
        self.value_position_set.push((value, position, d));
    }

    fn remove(&mut self, position: usize, value: usize, d: usize) {
        self.position_value_set.remove((position, value, d));
        self.value_position_set.remove((value, position, d));
    }

    fn get_min_value(&self) -> usize {
        // debug!("getmin", self.value_position_set.min());
        self.value_position_set.min().unwrap().0
    }

    fn debug(&self) {
        debug!("==");
        let mut ptr = self.position_value_set.min().unwrap();
        loop {
            debug!(ptr);
            if let Some(x) = self.position_value_set.peek_greater(ptr) {
                ptr = x;
            } else {
                break;
            }
        }
    }
}

fn main() {
    input! {
        h: usize, w: usize,
        ng_ranges: [(usize, usize); h]
    };
    let mut pset = PositionSet::new();
    pset.push(0, INF, 0);
    pset.push(1, 0, 0);
    pset.push(w+1, INF, 0);

    for i in 0..h {
        // pset.debug();

        // debug!(i, ng_ranges[i], pset.position_value_set.peek_less((ng_ranges[i].0, 0, 0)));
        let range_l = pset.position_value_set.peek_less((ng_ranges[i].0, 0, 0)).unwrap();
        let mut ptr = pset.position_value_set.peek_greater(range_l).unwrap();

        if range_l.0 < ng_ranges[i].0 && ng_ranges[i].1 < ptr.0 {
            if range_l.2 == 0 {
                pset.push(ng_ranges[i].0, range_l.1+1, 1);
                if ng_ranges[i].1+1 <= w {
                    pset.push(ng_ranges[i].1+1, range_l.1, 0);
                }
            }
        } else {
            loop {
                let next = pset.position_value_set.peek_greater(ptr).unwrap();
                if next.0 <= ng_ranges[i].1 {
                    pset.remove(ptr.0, ptr.1, ptr.2);
                    ptr = next;
                    continue;
                }
                // debug!(i, range_l, ptr, next, ng_ranges[i]);
                pset.remove(ptr.0, ptr.1, ptr.2);
                if range_l.2 == 0 {
                    pset.push(ng_ranges[i].0, range_l.1+1, 1);
                } else {
                    pset.push(range_l.0, range_l.1, range_l.2);
                }
                let mut nptr = ptr.clone();
                let mv = ng_ranges[i].1 + 1 - ptr.0;
                nptr.0 = ng_ranges[i].1 + 1;
                nptr.1 += ptr.2 * mv;
                // debug!("add?", nptr, ptr, next, mv);
                if nptr.0 < next.0 && nptr.0 <= w {
                    pset.push(nptr.0, nptr.1, nptr.2);
                }
                break;
            }
        }

        let ans = pset.get_min_value()+i+1;
        println!("{}", ifv!(ans >= INF, -1, ans as i64));
    }

    // pset.debug();
}