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 Python (3.4.3) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
from collections import defaultdict


class Prime:
    def __init__(self, number):  # N以下の素数
        self.jud = [True] * (number + 5)
        self.pri = []
        self.jud[0] = False
        self.jud[1] = False

        for i in range(number):
            if self.jud[i]:
                self.pri.append(i)
                for j in range(2, (number) // i + 1):
                    self.jud[i * j] = False

    def judge(self, x):
        return self.jud[x]

    def decom(self, x):
        s = x
        a = defaultdict(int)
        if s == 1:
            return a
        while s > 1:
            for p in self.pri:
                if s % p == 0:
                    a[p] += 1
                    s = s // p
                    break
        return a


N,M=map(int,input().split())
L=[tuple([int(i) for i in input().split()]) for i in range(N)]
Ki=Prime(M+1)
A=Ki.pri
#print(A)

def f(x):
    num=0
    for l,r in L:
        if l%x==0:
            num+=1
        elif r%x==0:
            num+=1
        elif l//x<r//x:
            num+=1
    return num

dd=defaultdict(int)
for a in A:
    for i in range(32):
        if pow(a,i)>M:
            break
        dd[pow(a,i)] = f(pow(a,i))
#print(dd)
print(dd[1])
for i in range(2,M+1):

    di=Ki.decom(i)
    L=[]
    for p,n in di.items():
        L.append(pow(p,n))
    ans=0
    t=len(L)
    if t==1:
        print(dd[i])
        continue
    for j in range(t<<1):
        num=0
        s=1
        coef=0
        for k in range(t):
            if j & (1<<k):
                s*=L[k]
                coef+=1
        if s==i:
            continue
        ans+=((-1)**(t-coef-1))*dd[s]
        #print(ans,coef,s,dd[s])
    dd[i]=ans
    print(ans)