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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.PrintWriter;
import java.util.Scanner;

public class Main {
  static Scanner sc = new Scanner(System.in);
  static PrintWriter writer = new PrintWriter(System.out);
  static final int TH = 200;

  public static void main(String[] args) {
    int N = sc.nextInt();
    int M = sc.nextInt();
    int[] sum = new int[M + 2];
    for (int i = 0; i < N; i++) {
      int L = Integer.parseInt(sc.next());
      int R = Integer.parseInt(sc.next());
      int prev = M + 100000;
      for (int j = 1; ; j++) {
        int l = L / j;
        int r = R / j;
        if (r < TH) break;
        sum[Math.max(TH, l)]++;
        if (r >= prev) {
          sum[prev]--;
        } else {
          sum[r + 1]--;
        }
        if (l < TH) break;
        prev = l;
      }
      for (int j = 1; j < Math.min(TH, M + 1); j++) {
        int lo = (L - 1) / j;
        int hi = R / j;
        if (lo != hi) {
          sum[j]++;
          sum[j + 1]--;
        }
      }
    }
    for (int i = 1; i <= M; i++) {
      sum[i] += sum[i - 1];
      writer.println(sum[i]);
    }
    writer.flush();
  }

}