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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<fstream>
#include<cstdio>
#include<string>
#include<algorithm>
#include<cmath>
#include<vector>
#include<stack>
#include<climits>
#include<cstring>
#include<queue>
#include<map>
#include<set>
#include<complex>
#include<typeinfo>
using namespace std;

typedef unsigned long long ull;
const int N_MAX = 300000;

struct raqSB{
    int dataSize;
    int bucketSize;
    ull data[N_MAX];
    ull bucket[N_MAX];

    raqSB(const int n){
        bucketSize = (int)sqrt(n) + 1;
        dataSize = bucketSize * bucketSize;
        for (int i=0;i<N_MAX;i++){
            data[i] = 0ull;
            bucket[i] = 0ull;
        }
    }

    void add(int s, int t, int x){
        int ss = s/bucketSize;
        int tt = t/bucketSize;
        if(ss==tt){
            for (int i=s;i<t+1;i++){
                data[i] += x;
            }
        }else{
            for(int i=s;i<(ss+1)*bucketSize;i++){
                data[i] += x;
            }
            for(int i=tt*bucketSize;i<t+1;i++){
                data[i] += x;
            }
            for(int i=ss+1;i<tt;i++){
                bucket[i] += x;
            }
        }
    }

    ull get(int i){
        return data[i] + bucket[i/bucketSize];
    }
};

struct Segment{
    int l, r;
    Segment(const int l, const int r): l(l), r(r) {}
};

int main(){
    int N, M, l, r;
    cin >> N >> M;
    vector< vector<Segment> > segList(M + 1);
    for (int i=0;i<N;i++){
        cin >> l >> r;
        Segment seg(l,r);
        segList[r-l+1].push_back(seg);
    }

    int A = N;
    int B;
    raqSB raqsb(M+1);
    for(int d=1;d<M+1;d++){
        B = 0;
        for (int k=1;d*k<M+1;k++){
            B += raqsb.get(d*k);
        }
        cout << A + B << endl;
        A -= segList[d].size();
        for(int m=0;m<segList[d].size();m++){
            raqsb.add(segList[d][m].l, segList[d][m].r, 1);
        }
    }
    return 0;
}