Problem Statement

There is a grid with $N$ rows and $M$ columns, and each cell contains a light bulb that can be freely switched on or off.
Here, for the bulb in the $i$-th row from the top and the $j$-th column from the left, we write

• when the bulb is on: $A_{i,j} = 1$
• when the bulb is off: $A_{i,j} = 0$

More precisely, output the number, modulo $998244353$, of ways to set the bulbs that satisfy the following condition.

• For every $j$ satisfying $1 \leq j \leq M-1$, the following condition holds:
• There are at least $K$ values of $i$ such that $A_{i,j} = 1$ and $A_{i,j+1} = 1$.

Input

$N\ M \ K$

• $1 \leq K \leq N \leq 5$
• $1 \leq M \leq 2 \times 10^4$
• All inputs are integers.

Output

Output the number, modulo $998244353$, of ways to set the bulbs that satisfy the condition. End the output with a newline.

Sample

2 2 1

7

3 4 1

1129

5 10 3

252507990