ABS Permutation (LIS ver.)

AtCoder

IDarc140_c

Time2000ms

Memory256MB

Difficulty—

The **happiness** of a permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,\dots,N)$ is defined as follows. * Let $A=(A_1,A_2,\ldots,A_{N-1})$ be a sequence of length $N-1$ with $A_i = |P_i-P_{i+1}|(1\leq i \leq N-1)$. The happiness of $P$ is the length of a longest strictly increasing subsequence of $A$. Print a permutation $P$ such that $P_1 = X$ with the greatest happiness. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq X \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X$ [samples]

Samples

Input #1

3 2

Output #1

2 1 3

Since $A=(1,2)$, the happiness of $P$ is $2$, which is the greatest happiness achievable, so the output meets the requirement.

Input #2

3 1

Output #2

1 2 3

Since $A=(1,1)$, the happiness of $P$ is $1$, which is the greatest happiness achievable, so the output meets the requirement.

API Response (JSON)

{
  "problem": {
    "name": "ABS Permutation (LIS ver.)",
    "description": {
      "content": "The **happiness** of a permutation $P=(P_1,P_2,\\ldots,P_N)$ of $(1,\\dots,N)$ is defined as follows. *   Let $A=(A_1,A_2,\\ldots,A_{N-1})$ be a sequence of length $N-1$ with $A_i = |P_i-P_{i+1}|(1\\leq ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc140_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The **happiness** of a permutation $P=(P_1,P_2,\\ldots,P_N)$ of $(1,\\dots,N)$ is defined as follows.\n\n*   Let $A=(A_1,A_2,\\ldots,A_{N-1})$ be a sequence of length $N-1$ with $A_i = |P_i-P_{i+1}|(1\\leq ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments