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: Time Limit Exceeded)

import java.io.PrintWriter;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		int N = sc.nextInt();
		int M = sc.nextInt();
		int[] l = new int[N];
		int[] r = new int[N];
		for(int i=0; i<N; i++) {
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();
		}

		int[] delta = new int[M+2];
		int[] ans = new int[M+1];
		
		for(int i=0; i<N; i++) {
			int lastMin = Integer.MAX_VALUE;
			for(int j=1; j<=M; j++) {
				int min = (l[i]+j-1)/j;
				int max = r[i]/j;
				if(min<=max) {
					if(max+1<lastMin) {
						if(lastMin<Integer.MAX_VALUE)
							delta[lastMin]++;
						delta[max+1]--;
					}
					lastMin = min;
					if(min<=r[i]-l[i]+1)
						break;
				}
			}
			delta[1]++;
		}
		
		
		int cur = 0;
		for(int i=1; i<=M; i++) {
			cur += delta[i];
			ans[i] += cur;
		}
		
		for(int i=1; i<=M; i++)
			pw.println(ans[i]);
		
		sc.close();
		pw.close();
	}
}