Title
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 li, li+1, li+2, ..., ri.
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 × 105
- 1 ≦ M ≦ 105
- 1 ≦ li ≦ ri ≦ M
Input
The input is given from Standard Input in the following format:
N M
l1 r1
:
lN rN
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