p03819 AtCoder Regular Contest 068 - Snuke Line
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.

Examples

Input

3 3
1 2
2 3
3 3


Output

3
2
2


Input

7 9
1 7
5 9
5 7
5 9
1 1
6 8
3 4


Output

7
6
6
5
4
5
5
3
2
```python
class BIT:
    def __init__(self, n):
        self.n = n
        self.bit = [0] * (n + 1)

    def add(self, k, x):
        while k <= self.n:
            self.bit[k] += x
            k += k & -k

    def sum(self, k):
        s = 0
        while k > 0:
            s += self.bit[k]
            k -= k & -k
        return s


n, m = map(int, input().split())
st = BIT(m)
L, R = [], []
d = [[] for i in range(m + 1)]
for i in range(n):
    l, r = map(int, input().split())
    L.append(l)
    R.append(r)
    d[r - l + 1].append(i)

num = n
for i in range(1, m + 1):
    num -= len(d[i])
    for j in d[i]:
        st.add(L[j], 1)
        st.add(R[j] + 1, -1)

    tmp = 0
    k = i
    for j in range(k, m + 1, i):
        tmp += st.sum(j)

    print(num + tmp)

```