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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

class FenwickTree(val n:Int, init:Int) {
  val dat = new Array[Int](n+1)
  for (i <- 1 to n) add(i, init)

  def this(n:Int) {
    this(n, 0)
  }

  def add(_idx:Int, value:Int) {
    var idx = _idx+1
    while(idx <= n) {
      dat(idx) += value
      idx += idx & -idx
    }
  }

  def query(_l:Int, _r:Int):Int = {
    var ans = 0
    var r = _r+1
    var l = _l+1
    while(r > 0) {
      ans += dat(r)
      r -= r & -r
    }
    while(l > 0) {
      ans -= dat(l)
      l -= l & -l
    }
    return ans
  }
}

object Main {
  def main(args: Array[String]) {
    val Array(n,m) = scala.io.StdIn.readLine().split(' ').map(_.toInt)
    val intervals = for(i <- Range(0,n).toArray) yield {
      val Array(l,r) = scala.io.StdIn.readLine().split(' ').map(_.toInt)
      Array((r-l+1), l, r)
    }
    var sortedInt = intervals.sortBy(_.apply(0))
    val ft = new FenwickTree(m+1)

    for(d <- 1 to m) {
      var count = 0
      val (before, after) = sortedInt.span(_.apply(0) < d)
      for (int <- before) {
        ft.add(int(1), 1)
        ft.add(int(2)+1, -1)
      }
      for(i <- Range(0, m+1, d)) count += ft.query(-1, i)
      count += after.length
      sortedInt = after
      println(count)
    }
  }
}