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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)


def bitadd(a,w,bit): #aにwを加える(1-origin)
 
    x = a
    while x <= (len(bit)-1):
        bit[x] += w
        x += x & (-1 * x)
 
def bitsum(a,bit): #ind 1～aまでの和を求める
 
    ret = 0
    x = a
    while x > 0:
        ret += bit[x]
        x -= x & (-1 * x)
    return ret


#区間更新BIT(BITを2つ用意し、BITの長さをN+2で初期化しておくべし)
def bitaddR(l,r,w,bit1,bit2): #半開区間[l,r)にwを加える

    bitadd(l,-1*w*l,bit1)
    bitadd(r,w*r,bit1)
    bitadd(l,w,bit2)
    bitadd(r,-1*w,bit2)

def bitsumR(r,bit1,bit2): #半開区間[1,r)の区間和

    return bitsum(r,bit1) + r * bitsum(r,bit2)


N,M = map(int,input().split())

bitA = [0] * (M+2)
bitB = [0] * (M+2)

len_LR = []

for i in range(N):

    l,r = map(int,input().split())
    len_LR.append([r-l,l,r])

len_LR.sort()
len_LR.append([float("inf"),0,float("inf")])
ind = 0
ns = N

for d in range(M):

    d += 1

    while len_LR[ind][2]-len_LR[ind][1]+1 < d:

        bitaddR(len_LR[ind][1] , len_LR[ind][2]+1 , 1 ,bitA,bitB)
        ns -= 1
        ind += 1

    np = 0

    for i in range(d,M+1,d):
        np += bitsumR(i+1,bitA,bitB) - bitsumR(i,bitA,bitB)

    print (ns + np)