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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let n: usize = s.next().unwrap().parse().unwrap();
	let m: usize = s.next().unwrap().parse().unwrap();
	let mut bit = BIT::new(m + 1);
	let mut q = vec![vec![]; m];
	for _ in 0..n {
		let l: usize = s.next().unwrap().parse().unwrap();
		let r: usize = s.next().unwrap().parse().unwrap();
		q[r - l].push((l, r));
	}

	use std::io::Write;
	let out = std::io::stdout();
	let mut out = std::io::BufWriter::new(out.lock());
	let mut f = n as i32;
	for d in 1..=m {
		writeln!(
			out,
			"{}",
			f + (d..=m).step_by(d).fold(0, |r, i| r + bit.sum(i + 1))
		)
		.unwrap();
		f -= q[d - 1].len() as i32;
		for &(l, r) in q[d - 1].iter() {
			bit.add(l, 1);
			bit.add(r + 1, -1);
		}
	}
}

pub struct BIT<T> {
	data: Vec<T>,
}

impl<T> BIT<T>
where
	T: Clone + Default + std::ops::Add<Output = T>,
{
	pub fn new(n: usize) -> Self {
		Self {
			data: vec![T::default(); n],
		}
	}

	pub fn sum(&self, i: usize) -> T {
		let mut r = T::default();
		let mut i = i;
		while i > 0 {
			r = r + self.data[i - 1].clone();
			i &= i - 1;
		}
		r
	}

	pub fn add(&mut self, i: usize, value: T) {
		let mut i = i;
		while i < self.data.len() {
			self.data[i] = self.data[i].clone() + value.clone();
			i |= i + 1;
		}
	}
}