Almost Sorted 2

AtCoder

IDabc431_f

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$ and a positive integer $D$. Find the number, modulo $998244353$, of integer sequences $B=(B_1, B_2, \ldots, B_N)$ that can be obtained by rearranging $A$ and satisfy the following condition: * $B_{i+1}\geq B_i-D$ holds for all $i\ (1\leq i\leq N-1)$. ## Constraints * $2\leq N\leq 2\times 10^5$ * $1\leq D\leq 10^6$ * $1\leq A_i\leq 10^6$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $D$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4 1
5 2 1 2

Output #1

3

The integer sequences satisfying the condition are $(1,2,2,5),(2,1,2,5),(2,2,1,5)$, which are three sequences.

Input #2

5 10
20 40 60 80 100

Output #2

Input #3

15 12345
18270 31252 27543 31406 22271 13402 12279 25697 18349 27615 39360 22790 32581 23990 36154

Output #3

858152905

API Response (JSON)

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    "name": "Almost Sorted 2",
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      "content": "You are given an integer sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$ and a positive integer $D$. Find the number, modulo $998244353$, of integer sequences $B=(B_1, B_2, \\ldots, B_N)$ that can be o",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
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    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$ and a positive integer $D$.\nFind the number, modulo $998244353$, of integer sequences $B=(B_1, B_2, \\ldots, B_N)$ that can be o...",
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      "language": "English"
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