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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.HashSet;
import java.util.Iterator;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.IntStream;

public class Main {
    
    private static class Pair {
        private int start;
        private int end;
        
        private Pair(int start) {
            this.start = start;
            this.end = start;
        }
        
        private int gap() {
            return end - start;
        }
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        final int H = sc.nextInt();
        final int W = sc.nextInt();
        
        final int[][] cannotDown = new int[H][2];
        
        for (int i = 0; i < H; i++) {
            cannotDown[i][0] = sc.nextInt() - 1;
            cannotDown[i][1] = sc.nextInt() - 1;
        }
        
        Set<Pair> ps = IntStream.range(0, W).mapToObj(Pair::new)
                .collect(HashSet::new, Set::add, Set::addAll);
        
        for (int i = 0; i < H; i++) {
            if (ps.isEmpty()) {
                System.out.println(-1);
                continue;
            }
            
            int min = Integer.MAX_VALUE;
            Iterator<Pair> itr = ps.iterator();
            
            while (itr.hasNext()) {
                Pair p = itr.next();
                
                if (cannotDown[i][0] <= p.end && p.end <= cannotDown[i][1]) {
                    if (cannotDown[i][1] == W - 1) {
                        itr.remove();
                        continue;
                    }
                    p.end = cannotDown[i][1] + 1;
                }
                if (p.gap() < min) {
                    min = p.gap();
                }
            }
            
            if (ps.isEmpty()) {
                System.out.println(-1);
            } else {
                System.out.println(min + i + 1);
            }
        }
    }
}