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)

use proconio::input;
use proconio::marker::Usize1;

fn is_ok(w: usize, ab: &[(usize, usize)], x: usize, ans: &mut Vec<usize>) -> bool {
    let mut updated = false;
    let mut count = 0_usize;
    let mut x = x;
    for (i, &(a_i, b_i)) in ab.iter().enumerate() {
        count += 1;
        let d = if x < a_i {
            0
        } else if b_i < w {
            b_i - x
        } else {
            break;
        };
        x += d as usize;
        count += d;
        if count < ans[i] {
            ans[i] = count;
            updated = true;
        }
    }
    updated
}

fn main() {
    input! {
        h: usize,
        w: usize,
        ab: [(Usize1, usize); h],
    };
    let inf = 1_000_000_000_usize;
    let mut ans = vec![inf; h];

    {
        let mut r = 0;
        for (i, &(_, b_i)) in ab.iter().enumerate() {
            if b_i > r {
                r = b_i;
            }
            if r == w {
                break;
            }
            ans[i] = i;
        }
    }

    let mut l = 0;
    let mut r = w;
    while r - l > 0 {
        let m = l + (r - l) / 2;
        if is_ok(w, &ab, m, &mut ans) {
            l = m;
        } else {
            r = m;
        }
    }
    for &ans_i in ans.iter() {
        println!("{}", if ans_i == inf { -1 } else { ans_i as i64 });
    }
}