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)

use std::cmp;
use std::cmp::Reverse;
use std::collections::{BTreeMap, BinaryHeap};

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let h: i64 = sc.read();
    let w: i64 = sc.read();

    let mut dist = BTreeMap::new();
    let mut heap = BinaryHeap::new();
    for i in 1..=w {
        dist.insert(i, 0);
        heap.push((Reverse(0), i));
    }
    for depth in 1..=h {
        let left: i64 = sc.read();
        let right: i64 = sc.read();
        while let Some((&cur_pos, &cur_cost)) = dist.range(left..=right).next_back() {
            let next_pos = right + 1;
            let next_cost = right + 1 - cur_pos + cur_cost;
            assert_eq!(dist.remove(&cur_pos), Some(cur_cost));
            if next_pos <= w {
                let cur = dist.entry(next_pos).or_insert(1 << 50);
                if *cur > next_cost {
                    *cur = next_cost;
                    heap.push((Reverse(next_cost), next_pos));
                }
            }
        }

        let mut ans = None;
        while let Some((Reverse(cost), pos)) = heap.pop() {
            if let Some(&stored_cost) = dist.get(&pos) {
                if stored_cost == cost {
                    ans = Some(stored_cost);
                    heap.push((Reverse(stored_cost), pos));
                    break;
                }
            }
        }

        if let Some(ans) = ans {
            sc.write(ans + depth);
        } else {
            sc.write("-1");
        }
        sc.write('\n');
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write_all(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}