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 = 'class BIT(object):\n    def __init__(self, size):\n        self.size = size\n        self.bit = [0] * (self.size + 1)\n\n    def sum(self, i):\n        s = 0\n        while i > 0:\n            s += self.bit[i]\n            i -= i & -i\n        return s\n\n    def add(self, i, x):\n        while i <= self.size:\n            self.bit[i] += x\n            i += i & -i\n\n    def __str__(self):\n        return str(self.bit)\n\nn, m = list(map(int,input().split()))\nlr = [[] for i in range(m + 1)]\nfor i in range(n):\n    l, r = list(map(int,input().split()))\n    lr[r - l + 1].append(l)\n\nbit = BIT(m + 1)\nt = 0\nfor d in range(1, m + 1):\n    for l in lr[d]:\n        #print(l, l + d)\n        bit.add(l, 1)\n        #print(bit.bit)\n        bit.add(l + d, -1)\n        #print(bit.bit)\n\n    t += len(lr[d])\n    ans = n - t\n\n    cur = 0\n    while cur <= m:\n        # bitの0 ~ curまでの総和を加算\n        ans += bit.sum(cur)\n        cur += d\n\n    print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16645