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 (1.15.1) (judge verdict: Accepted)

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let m: usize = sc.read();

    let mut s = vec![];
    for _ in 0..n {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let w = r - l + 1;
        s.push((w, l, r));
    }

    s.sort();
    let mut seg = range_add_segment_tree::RangeAddSegmentTree::new();
    for i in 0..(m + 1) {
        seg.update(i, 0);
    }
    let mut head = 0;
    for d in 1..(m + 1) {
        while head < n && s[head].0 < d {
            let (_, l, r) = s[head];
            seg.add(l, r + 1, 1);
            head += 1;
        }
        let mut ans = (n - head) as i64;
        let mut pos = 0;
        while pos <= m {
            ans += seg.get_max(pos, pos + 1);
            pos += d;
        }

        println!("{}", ans);
    }
}
pub mod range_add_segment_tree {

    use std::cmp;
    pub const NUM: usize = 1 << 20;
    pub const INF: i64 = 1 << 60;

    pub struct RangeAddSegmentTree {
        seg_min: Vec<i64>,
        seg_max: Vec<i64>,
        seg_add: Vec<i64>,
    }

    impl RangeAddSegmentTree {
        pub fn new() -> Self {
            RangeAddSegmentTree {
                seg_min: vec![INF; NUM * 2],
                seg_max: vec![-INF; NUM * 2],
                seg_add: vec![0; NUM * 2],
            }
        }

        /// add to [a, b)
        pub fn add(&mut self, a: usize, b: usize, value: i64) {
            self.add_to_range(a, b, value, 0, 0, NUM);
        }

        fn add_to_range(
            &mut self,
            a: usize,
            b: usize,
            value: i64,
            k: usize,
            left: usize,
            right: usize,
        ) {
            if b <= left || right <= a {
                return;
            }
            if a <= left && right <= b {
                let mut k = k;
                self.seg_add[k] += value;
                while k > 0 {
                    k = (k - 1) / 2;
                    self.seg_min[k] = cmp::min(
                        self.seg_min[k * 2 + 1] + self.seg_add[k * 2 + 1],
                        self.seg_min[k * 2 + 2] + self.seg_add[k * 2 + 2],
                    );
                    self.seg_max[k] = cmp::max(
                        self.seg_max[k * 2 + 1] + self.seg_add[k * 2 + 1],
                        self.seg_max[k * 2 + 2] + self.seg_add[k * 2 + 2],
                    );
                }
            } else {
                self.add_to_range(a, b, value, k * 2 + 1, left, (left + right) / 2);
                self.add_to_range(a, b, value, k * 2 + 2, (left + right) / 2, right);
            }
        }

        pub fn update(&mut self, pos: usize, value: i64) {
            let mut k = pos + NUM - 1;
            self.seg_min[k] = value;
            self.seg_max[k] = value;
            while k > 0 {
                k = (k - 1) / 2;
                self.seg_min[k] = cmp::min(self.seg_min[k * 2 + 1], self.seg_min[k * 2 + 2]);
                self.seg_max[k] = cmp::max(self.seg_max[k * 2 + 1], self.seg_max[k * 2 + 2]);
            }
        }

        pub fn get_min(&self, a: usize, b: usize) -> i64 {
            get(
                &self.seg_min,
                &self.seg_add,
                INF,
                a,
                b,
                0,
                0,
                NUM,
                &cmp::min,
            )
        }

        pub fn get_max(&self, a: usize, b: usize) -> i64 {
            get(
                &self.seg_max,
                &self.seg_add,
                -INF,
                a,
                b,
                0,
                0,
                NUM,
                &cmp::max,
            )
        }
    }

    fn get<F>(
        seg: &Vec<i64>,
        add: &Vec<i64>,
        default_value: i64,
        a: usize,
        b: usize,
        k: usize,
        left: usize,
        right: usize,
        f: &F,
    ) -> i64
    where
        F: Fn(i64, i64) -> i64,
    {
        if b <= left || right <= a {
            default_value
        } else if a <= left && right <= b {
            seg[k] + add[k]
        } else {
            let mid = (left + right) / 2;
            let x = get(seg, add, default_value, a, b, k * 2 + 1, left, mid, f);
            let y = get(seg, add, default_value, a, b, k * 2 + 2, mid, right, f);
            f(x, y) + add[k]
        }
    }
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}