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"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func Scan() string {
	sc.Scan()
	return sc.Text()
}
func iScan() int {
	n, _ := strconv.Atoi(Scan())
	return n
}
func fScan() float64 {
	n, _ := strconv.ParseFloat(Scan(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func SScan(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scan()
	}
	return a
}
func iSScan(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = iScan()
	}
	return a
}
func abs(x int) int {
	if x < 0 {
		x = -x
	}
	return x
}
func larger(a, b int) int {
	if a < b {
		return b
	} else {
		return a
	}
}
func smaller(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}
func max(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x < a[i] {
			x = a[i]
		}
	}
	return x
}
func min(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x > a[i] {
			x = a[i]
		}
	}
	return x
}
func sum(a []int) int {
	x := 0
	for _, v := range a {
		x += v
	}
	return x
}
func fSum(a []float64) float64 {
	x := 0.
	for _, v := range a {
		x += v
	}
	return x
}

var mod int = 1000000007

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, mod)
	sc.Split(bufio.ScanWords)
	h, w := iScan(), iScan()
	from := make([][]int, w)
	for i := 0; i < w; i++ {
		from[i] = []int{i + 1, i + 1}
	}
	for i := 0; i < h; i++ {
		a, b := iScan(), iScan()
		d := make(map[int]int)
		for _, v := range from {
			if a <= v[0] && v[0] <= b {
				if b+1 <= w {
					if _, ok := d[b+1]; ok {
						d[b+1] = larger(d[b+1], v[1])
					} else {
						d[b+1] = v[1]
					}
				}
			} else {
				d[v[0]] = v[1]
			}
		}
		from = make([][]int, 0, w)
		ans := mod * mod
		for k, v := range d {
			from = append(from, []int{k, v})
			ans = smaller(ans, i+1+k-v)
		}
		if ans == mod*mod {
			fmt.Println(-1)
		} else {
			fmt.Println(ans)
		}
	}
}