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-----
3 3
1 2
2 3
3 3

-----Sample Output-----
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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "import sys\nfrom operator import itemgetter\n\nmod = 10**9 + 7\ninf = 1<<30\n\ndef solve():\n    N, M = map(int, sys.stdin.readline().split())\n    sects = []\n\n    for i in range(N):\n        li, ri = map(int, sys.stdin.readline().split())\n\n        sects.append((li - 1, ri, ri - li + 1))\n\n    sects.sort(key=itemgetter(2))\n\n    # print(sects)\n\n    print(N)\n\n    left = 0\n\n    ft = FenwickTree([0]*(M + 1))\n\n    for d in range(2, M + 1):\n        for j in range(left, N):\n            if sects[j][2] >= d:\n                left = j\n                break\n            else:\n                ft.add(sects[j][0], 1)\n                ft.add(sects[j][1], -1)\n        else:\n            left = N\n\n        # print('left', left)\n        # print(ft.data)\n\n        ans = N - left + sum(ft.get_sum(j) for j in range(d, M + 1, d))\n        \n        print(ans)\n\nclass FenwickTree:\n    def __init__(self, a):\n        self.n = len(a)\n        self.data = [0] + a[:]\n\n        for i in range(1, self.n + 1):\n            if i + (i & (-i)) <= self.n:\n                self.data[i + (i & (-i))] += self.data[i]\n\n    def add(self, i, x):\n        ''' a[i] += x '''\n        i += 1 # 0-oringn -> 1-origin\n\n        while i <= self.n:\n            self.data[i] += x\n            i += i & (-i)\n\n    def get_sum(self, r):\n        ''' sum[a_0 .. a_r) '''\n        res = 0\n\n        while r > 0:\n            res += self.data[r]\n            r -= r & (-r)\n\n        return res\n\n\ndef __starting_point():\n    solve()\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17795