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)

// ---------- begin multiset ----------
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);
        }
    }
}
// ---------- end multiset ----------

use proconio::marker::*;
use proconio::*;
use std::cmp::*;
use std::collections::*;
use std::ops::Bound::*;

#[fastout]
fn run() {
    input! {
        h: usize,
        w: usize,
        p: [(Usize1, usize); h],
    }
    let mut map = BTreeMap::new();
    let mut set = MultiSet::new();
    for i in 0..w {
        map.insert(i, 0);
        set.insert(0usize);
    }
    for (i, &(l, r)) in p.iter().enumerate() {
        let mut del = vec![];
        for (&k, &v) in map.range((Included(&l), Included(&r))) {
            set.remove(&v);
            del.push((k, v + r - k));
        }
        for &(k, _) in del.iter() {
            map.remove(&k);
        }
        if r < w {
            if let Some(v) = del.iter().map(|p| p.1).min() {
                map.insert(r, v);
                set.insert(v);
            }
        }
        if let Some(&v) = set.map.keys().next() {
            println!("{}", v + i + 1);
        } else {
            println!("-1");
        }
    }
}

fn main() {
    run();
}