≥ K

AtCoder

IDarc148_e

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of length $N$, $A = (A_1, ..., A_N)$, and an integer $K$. How many permutations of $A$ are there such that no two adjacent elements sum to less than $K$? Find the count modulo $998244353$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $0 \leq K \leq 10^9$ * $0 \leq A_i \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4 5
1 2 3 4

Output #1

4

The following four permutations satisfy the condition:

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

Input #2

4 3
1 2 3 3

Output #2

12

There are $12$ permutations of $A$, all of which satisfy the condition.

Input #3

10 7
3 1 4 1 5 9 2 6 5 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "≥ K",
    "description": {
      "content": "You are given a sequence of length $N$, $A = (A_1, ..., A_N)$, and an integer $K$.   How many permutations of $A$ are there such that no two adjacent elements sum to less than $K$? Find the count modu",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc148_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of length $N$, $A = (A_1, ..., A_N)$, and an integer $K$.  \nHow many permutations of $A$ are there such that no two adjacent elements sum to less than $K$? Find the count modu...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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