Home

Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

You are given an integer $M$ and $N$ pairs of integers $(A_1, B_1), (A_2, B_2), \dots, (A_N, B_N)$.
For all $i$, it holds that $1 \leq A_i \lt B_i \leq M$.

A sequence $S$ is said to be a good sequence if the following conditions are satisfied:

  • $S$ is a contiguous subsequence of the sequence $(1,2,3,..., M)$.
  • For all $i$, $S$ contains at least one of $A_i$ and $B_i$.

Let $f(k)$ be the number of possible good sequences of length $k$.
Enumerate $f(1), f(2), \dots, f(M)$.

Constraints

  • $1 \leq N \leq 2 \times 10^5$
  • $2 \leq M \leq 2 \times 10^5$
  • $1 \leq A_i \lt B_i \leq M$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_N$ $B_N$

Output

Print the answers in the following format:

$f(1)$ $f(2)$ $\dots$ $f(M)$

Sample Input 1

3 5
1 3
1 4
2 5

Sample Output 1

0 1 3 2 1

Here is the list of all possible good sequences.

  • $(1,2)$
  • $(1,2,3)$
  • $(2,3,4)$
  • $(3,4,5)$
  • $(1,2,3,4)$
  • $(2,3,4,5)$
  • $(1,2,3,4,5)$

Sample Input 2

1 2
1 2

Sample Output 2

2 1

Sample Input 3

5 9
1 5
1 7
5 6
5 8
2 6

Sample Output 3

0 0 1 2 4 4 3 2 1