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: Time Limit Exceeded)

// use superslice::Ext;

/*
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::<std::collections::HashSet<(usize, usize)>>();

    /*
    let mut costs = (vec![0; w])
        .iter()
        .collect::<std::collections::BinaryHeap<i64>>();
    */

    let mut y = 0;

    for arg in ab.iter() {
        let src = nodes
            .iter()
            .fold(-1, |val, &node| {
                return if arg.0 <= node.0 && node.0 <= arg.1 { val.max(node.1 as i64) } else { val };
            });

        if src != -1 && arg.1 + 1 <= w {
            nodes.insert((arg.1 + 1, src as usize));
        }

        nodes.retain(|&x| x.0 < arg.0 || arg.1 < x.0);

        let ans = nodes
            .iter()
            .map(|&x| (x.0 - x.1 + y + 1) as i64)
            .min()
            .unwrap_or(-1);

        println!("{}", ans);

        y += 1;
    }
}