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)

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut lhs = 0;
        let mut rhs = self.len();

        while lhs != rhs {
            let mid = (lhs + rhs) / 2;
            match self[mid].cmp(x) {
                std::cmp::Ordering::Less => { lhs = mid + 1; }
                std::cmp::Ordering::Equal | std::cmp::Ordering::Greater => { rhs = mid; }
            }
        }
        lhs
    }
}

fn main() {
    proconio::input! {
        h: usize,
        w: usize,
        ab: [(usize, usize); h]
    }

    let mut nodes = (1..=w)
        .map(|x: usize| (x, x))
        .collect::<Vec<(usize, usize)>>();

    for i in 0..h {
        let arg = ab[i];
        nodes.sort_by(|&a, &b| a.0.cmp(&b.0));

        let min_arg = (arg.0, 0);
        let index = nodes.lower_bound(&min_arg);

        if index < nodes.len() && arg.1 != w {
            nodes.push((arg.1 + 1, nodes[index].1));
        }

        while index < nodes.len() {
            if arg.1 < nodes[index].0 { break }
            nodes.remove(index);
        }

        let cost = nodes.iter()
            .map(|&ab| (ab.0 as i64) - (ab.1 as i64) + (i as i64) + 1)
            .min()
            .unwrap_or(-1);

        println!("{}", cost)
    }
}