Rampant Growth

Time limit1sMemory limit2048 MB

Summary

Count the ways to place exactly one plant per column in an r by c grid so that plants in adjacent columns sit in different rows, modulo 998244353.

Level: Easy2 of 10
Topics: Math, Combinatorics
Solved: No attempts yet

Problem

Eddy is planning his garden, which is a grid. He wants exactly one plant in each column. To keep the plants from competing for resources, plants in adjacent columns must be in different rows.

Count the number of ways Eddy can place plants in his garden under these conditions. Two ways differ if some square has a plant in one arrangement but not in the other. Output the count modulo $998\,244\,353$ .

Input

The single line of input contains two space-separated integers $r$ and $c$ ( $1 \leq r,c\leq 50$ ), where $r$ is the number of rows in Eddy's garden grid and $c$ is the number of columns.

Output

Output a single integer, the number of ways Eddy can place plants in his garden, modulo $998\,244\,353$ .

Examples3

Example 1
Input
```
3 2
```
Expected output
```
6
```
Example 2
Input
```
1 5
```
Expected output
```
0
```
Example 3
Input
```
42 25
```
Expected output
```
722210361
```