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 mut sc = Scanner::new();
    let n: usize = sc.read();
    let m: usize = sc.read();

    let mut intervals: Vec<(usize, usize, usize)> = vec![];
    for _ in 0..n {
        let l: usize = sc.read();
        let r: usize = sc.read();
        let d = r - l + 1;
        intervals.push((d, l, r));
    }
    intervals.sort();

    let mut seg = tree::RangeAddSegmentTree::new();
    for i in 0..(m + 1) {
        seg.update(i, 0);
    }

    let mut head = 0;
    for cur_d in 1..(m + 1) {
        while head < intervals.len() {
            let (d, l, r) = intervals[head];
            if d < cur_d {
                seg.add(l, r + 1, 1);
                head += 1;
            } else {
                break;
            }
        }

        let rest = (intervals.len() - head) as i64;
        let mut ans = rest;
        for i in 0..m {
            if i * cur_d + 1 > m + 1 {
                break;
            }
            ans += seg.get_max(i * cur_d, i * cur_d + 1);
        }
        println!("{}", ans);
    }
}

mod tree {
    use std::cmp;
    const NUM: usize = 1 << 20;
    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 {
            self.get_min_range(a, b, 0, 0, NUM)
        }

        fn get_min_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> i64 {
            if b <= left || right <= a {
                INF
            } else if a <= left && right <= b {
                self.seg_min[k] + self.seg_add[k]
            } else {
                let x = self.get_min_range(a, b, k * 2 + 1, left, (left + right) / 2);
                let y = self.get_min_range(a, b, k * 2 + 2, (left + right) / 2, right);
                cmp::min(x, y) + self.seg_add[k]
            }
        }

        pub fn get_max(&self, a: usize, b: usize) -> i64 {
            self.get_max_range(a, b, 0, 0, NUM)
        }

        fn get_max_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> i64 {
            if b <= left || right <= a {
                -INF
            } else if a <= left && right <= b {
                self.seg_max[k] + self.seg_add[k]
            } else {
                let x = self.get_max_range(a, b, k * 2 + 1, left, (left + right) / 2);
                let y = self.get_max_range(a, b, k * 2 + 2, (left + right) / 2, right);
                cmp::max(x, y) + self.seg_add[k]
            }
        }
    }

}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}