At Least One

AtCoder

IDabc260_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

0 1 3 2 1

Here is the list of all possible good sequences.

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

Input #2

1 2
1 2

Output #2

2 1

Input #3

Output #3

0 0 1 2 4 4 3 2 1

API Response (JSON)

{
  "problem": {
    "name": "At Least One",
    "description": {
      "content": "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 sequ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc260_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $M$ and $N$ pairs of integers $(A_1, B_1), (A_2, B_2), \\dots, (A_N, B_N)$.  \nFor all $i$, it holds that $1 \\leq A_i \\lt B_i \\leq M$.\nA sequence $S$ is said to be a **good sequ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments