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: Wrong Answer)

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 = RangeBIT::new(m + 1);
	for _ in 0..n {
		use num::integer::Roots;
		let l: usize = s.next().unwrap().parse().unwrap();
		let r: usize = s.next().unwrap().parse().unwrap();
		let mut j = vec![];
		for i in 1..=n.sqrt() + 1 {
			j.push(i);
			j.push((l - 1) / i + 1);
			j.push(r / i + 1);
		}
		j.sort();
		j.dedup();
		for i in 0..j.len() - 1 {
			let a = (l - 1) / j[i];
			let b = r / j[i];
			if a < b {
				bit.range_add(j[i], j[i + 1], 1);
			}
		}
	}

	use std::io::Write;
	let out = std::io::stdout();
	let mut out = std::io::BufWriter::new(out.lock());
	for i in 1..=m {
		writeln!(out, "{}", bit.range_sum(i, i + 1)).unwrap();
	}
}

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 construct(a: Vec<T>) -> Self {
		let mut a = a;
		for i in 0..a.len() {
			if i | (i + 1) >= a.len() {
				continue;
			}
			let v = a[i].clone();
			a[i | (i + 1)] = a[i | (i + 1)].clone() + v;
		}
		Self { data: a }
	}

	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;
		}
	}
}

pub struct RangeBIT<T> {
	data0: BIT<T>,
	data1: BIT<T>,
}

impl<T> RangeBIT<T>
where
	T: Clone
		+ Default
		+ std::ops::Add<Output = T>
		+ std::ops::Sub<Output = T>
		+ std::ops::Mul<Output = T>
		+ std::ops::Neg<Output = T>
		+ std::convert::TryFrom<usize>,
	<T as std::convert::TryFrom<usize>>::Error: std::fmt::Debug,
{
	pub fn new(n: usize) -> Self {
		Self {
			data0: BIT::new(n),
			data1: BIT::new(n),
		}
	}

	pub fn range_add(&mut self, l: usize, r: usize, value: T) {
		self.data0.add(l, -value.clone() * T::try_from(l).unwrap());
		self.data0.add(r, value.clone() * T::try_from(r).unwrap());
		self.data1.add(l, value.clone());
		self.data1.add(r, -value);
	}

	pub fn range_sum(&self, l: usize, r: usize) -> T {
		self.query(r) - self.query(l)
	}

	pub fn query(&self, r: usize) -> T {
		self.data0.sum(r) + T::try_from(r).unwrap() * self.data1.sum(r)
	}
}