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 proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;

#[derive(Clone, Debug, Default)]
struct Struct;

//#[proconio::fastout]
fn main() {
    input! {
        h: usize,
        w:usize,
        ab: [(Usize1,Usize1);h],
    }

    const MAX_WALK: usize = 200005;
    let mut m = BTreeMap::new();
    for i in 0..w {
        m.insert(i, 0);
    }

    let mut w_hist = vec![0; MAX_WALK + 1];
    w_hist[0] = w;
    w_hist[MAX_WALK] = 1;

    let mut v = Vec::with_capacity(w);
    let mut ans = 0;

    for i in 0..h {
        let l = ab[i].0;
        let r = ab[i].1 + 1;
        v.clear();
        let mut min_walk = MAX_WALK;
        for (&pos, &walk) in m.range(l..r + 1) {
            min_walk = min(min_walk, walk + (r - pos));
            v.push(pos);
            w_hist[walk] -= 1;
        }
        for pos in &v {
            m.remove(pos);
        }
        if min_walk != MAX_WALK && r < w {
            m.insert(r, min_walk);
            w_hist[min_walk] += 1;
        }

        // for j in 0..w {
        //     if let Some(wa) = m.get(&j) {
        //         print!("{} ", wa);
        //     } else {
        //         print!("x ",);
        //     }
        // }
        // println!("--{}", ans);

        while w_hist[ans] == 0 {
            ans += 1;
        }

        if ans == MAX_WALK {
            println!("{}", -1);
        } else {
            println!("{}", ans + i + 1);
        }
    }
}