200682: [AtCoder]ARC068 E - Snuke Line

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

有一趟列车有 M+1 个车站,从 0 到 M 编号。有 N 种商品,第 i 种只在编号 [li,ri] 的车站出售。一辆列车有一个预设好的系数 d,从 0 出发,只会在 d 的倍数车站停车。对于 d 从 1 到 M 的列车,求最多能买到多少种商品。

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