Sum of Fibonacci Sequence

AtCoder

IDs8pc_3_g

Time2000ms

Memory256MB

Difficulty—

E869120 defined a sequence $a$ like this: * $a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \\ (k \\ge 1)$ He also defined sequences $d_1, d_2, d_3, \\dots , d_n$, as the following recurrence relation : * $d_{1, j} = a_j$ * $d_{i, j} = \\sum_{k = 1}^j d_{i - 1, k} \\ (i \\ge 2)$ You are given integers $n$ and $m$. Please calculate the value of $d_{n, m}$. Since the answer can be large number, print the answer modulo $998,244,353$. Can you solve this problem??? ## Input The input is given from standard input in the following format. > $n \\quad m$ [samples]

Samples

Input #1

4 7

Output #1

176

The sequence is following:  

$d_{i, 1}$

$d_{i, 2}$

$d_{i, 3}$

$d_{i, 4}$

$d_{i, 5}$

$d_{i, 6}$

$d_{i, 7}$

$d_1$

1

1

2

3

5

8

13

$d_2$

1

2

4

7

12

20

33

$d_3$

1

3

7

14

26

46

79

$d_4$

1

4

11

25

51

97

176

  
As a result, the answer is $d_{4, 7} = 176$.

Input #2

12 20

Output #2

174174144

Input #3

16 30

Output #3

102292850

You can calculate that $d_{16, 30} = 1,193,004,294,685$.  
Please don't forget printing the answer mod $998,244,353$.

API Response (JSON)

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  "problem": {
    "name": "Sum of Fibonacci Sequence",
    "description": {
      "content": "E869120 defined a sequence $a$ like this:   *   $a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \\\\ (k \\\\ge 1)$    He also defined sequences $d_1, d_2, d_3, \\\\dots , d_n$, as the following recurrence relation :   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "s8pc_3_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "E869120 defined a sequence $a$ like this:  \n\n*   $a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \\\\ (k \\\\ge 1)$\n\n  \nHe also defined sequences $d_1, d_2, d_3, \\\\dots , d_n$, as the following recurrence relation :  \n...",
      "is_translate": false,
      "language": "English"
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