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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	} else {
		return b
	}
}

func main() {
	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)

	h := nextInt()
	w := nextInt()
	s0 := make(map[int]int)
	for i := 1; i <= w; i++ {
		s0[i] = 0
	}

	for k := 1; k <= h; k++ {
		a := nextInt()
		b := nextInt()

		s1 := make(map[int]int)

		for pos, c := range s0 {
			if pos < a || pos > b {
				p, ok := s1[pos]
				if ok {
					s1[pos] = min(p, c)
				} else {
					s1[pos] = c
				}
			} else if b < w {
				p, ok := s1[b+1]
				if ok {
					s1[b+1] = min(p, c+b+1-pos)
				} else {
					s1[b+1] = c + b + 1 - pos
				}
			}
		}

		if len(s1) == 0 {
			for j := k; j <= h; j++ {
				fmt.Println(-1)
			}
			break
		}

		m := math.MaxInt32
		for _, x := range s1 {
			m = min(m, x)
		}

		fmt.Println(m + k)
		s0 = s1
	}
}