Problem:
Score : 700 points

Problem Statement

Snuke has decided to play a game, where the player runs a railway company.
There are M+1 stations on Snuke Line, numbered 0 through M.
A train on Snuke Line stops at station 0 and every d-th station thereafter, where d is a predetermined constant for each train.
For example, if d = 3, the train stops at station 0, 3, 6, 9, and so forth.

There are N kinds of souvenirs sold in areas around Snuke Line. The i-th kind of souvenirs can be purchased when the train stops at one of the following stations: stations l_i, l_i+1, l_i+2, ..., r_i.

There are M values of d, the interval between two stops, for trains on Snuke Line: 1, 2, 3, ..., M.
For each of these M values, find the number of the kinds of souvenirs that can be purchased if one takes a train with that value of d at station 0.
Here, assume that it is not allowed to change trains.

Constraints

1 ≦ N ≦ 3 × 10^{5}

1 ≦ M ≦ 10^{5}

1 ≦ l_i ≦ r_i ≦ M

Input

The input is given from Standard Input in the following format:

N M
l_1 r_1
:
l_{N} r_{N}

Output

Print the answer in M lines. The i-th line should contain the maximum number of the kinds of souvenirs that can be purchased if one takes a train stopping every i-th station.

Sample Input 1

3 3
1 2
2 3
3 3

Sample Output 1

3
2
2

If one takes a train stopping every station, three kinds of souvenirs can be purchased: kind 1, 2 and 3.

If one takes a train stopping every second station, two kinds of souvenirs can be purchased: kind 1 and 2.

If one takes a train stopping every third station, two kinds of souvenirs can be purchased: kind 2 and 3.

Sample Input 2

7 9
1 7
5 9
5 7
5 9
1 1
6 8
3 4

Sample Output 2

7
6
6
5
4
5
5
3
2

Solution in Go (1.6) (judge verdict: Accepted)

package main

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

var sc = bufio.NewScanner(os.Stdin)

// Binary indexed tree

type BITree struct {
	bit []int
	M int
}

func newBITree(m int) *BITree {
	b := new(BITree)
	b.M = m
	b.bit = make([]int, m + 1)
	return b
}

func (b BITree) sum(i int) int {
	if (i <= 0) {
		return 0
	}
	return b.bit[i] + b.sum(i - (-i & i))
}

func (b BITree) add(i int, x int) {
	if (i > b.M) {
		return
	}
	b.bit[i] += x
	b.add(i + (-i & i), x)
}

type Section struct {
	start int
	end int
}

func main() {
	N, M, l, r := scan()

	// 区間[l,r]を長さによって分類する
	sectionsGroup := make([][]Section, M + 1)
	for i := 0; i <= M; i++ {
		sectionsGroup[i] = make([]Section, 0)
	}
	for n := 0; n < N; n++ {
		length := r[n] - l[n] + 1
		section := Section{
			start: l[n],
			end: r[n],
		}
		sectionsGroup[length] = append(sectionsGroup[length], section)
	}

	// 必ず通る区間たち
	base := N
	// Binary indexed tree
	bit := newBITree(M+2)

	answers := make([]int, M + 1)

	// BIT使って頑張る
	for d := 1; d <= M; d++ {
		sections := sectionsGroup[d - 1]
		for _, section := range sections {
			start := section.start
			end := section.end
			bit.add(start, 1)
			bit.add(end + 1, -1)
		}
		base -= len(sections)
		answers[d] = base
		for pos := 0; pos <= M; pos += d {
			answers[d] += bit.sum(pos)
		}
	}

	for d := 1; d <= M; d++ {
		fmt.Println(answers[d])
	}
}


func scan() (int, int, []int, []int) {
	var N, M int
	sc.Scan()
	nm := strings.Split(sc.Text(), " ")
	N, _ = strconv.Atoi(nm[0])
	M, _ = strconv.Atoi(nm[1])
	l := make([]int, N)
	r := make([]int, N)
	for i := 0; i < N; i++ {
		sc.Scan()
		lr := strings.Split(sc.Text(), " ")
		l[i], _ = strconv.Atoi(lr[0])
		r[i], _ = strconv.Atoi(lr[1])
	}
	return N, M, l, r
}