String Construction

Interview

Time limit1sMemory limit1024 MB

Summary

Count the pairs of length-N uppercase strings whose longest common subsequence made only of 'A' has length exactly M, modulo 998244353.

Level: Medium4 of 10
Topics: Math, Combinatorics, Implementation
Solved: No attempts yet

Problem

Using uppercase English letters, build two strings $S_1$ and $S_2$ of length $N$ .

For a string $S$ , a subsequence is a new string made by deleting zero or more characters from $S$ . A string that is a common subsequence of $S_1$ and $S_2$ and consists only of A is called a common A-subsequence. Count the number of ways to build $S_1$ and $S_2$ so that the longest common A-subsequence has length exactly $M$ .

Input

The first line contains two integers $N$ and $M$ , separated by a space.

Output

On the first line, print the answer modulo $998\,244\,353$ .

Constraints

$1 \le M \le N \le 2 \times 10^5$

Examples2

Example 1
Input
```
2 1
```
Expected output
```
2600
```
Example 2
Input
```
2023 12
```
Expected output
```
139579432
```