Problem Statement

Takahashi is playing sugoroku, a board game.

The board has ~N+1~ squares, numbered ~0~ to ~N~ . Takahashi starts at square ~0~ and goes for square ~N~ .

The game uses a roulette wheel with ~M~ numbers from ~1~ to ~M~ that appear with equal probability. Takahashi spins the wheel and moves by the number of squares indicated by the wheel. If this would send him beyond square ~N~ , he turns around at square ~N~ and goes back by the excessive number of squares.

For instance, assume that ~N=4~ and Takahashi is at square ~3~ . If the wheel shows ~4~ , the excessive number of squares beyond square ~4~ is ~3+4-4=3~ . Thus, he goes back by three squares from square ~4~ and arrives at square ~1~ .

When Takahashi arrives at square ~N~ , he wins and the game ends.

Find the probability, modulo ~998244353~ , that Takahashi wins when he may spin the wheel at most ~K~ times.

How to print a probability modulo ~998244353~

It can be proved that the sought probability is always a rational number. Additionally, under the Constraints of this problem, when the sought probability is represented as an irreducible fraction ~\frac{y}{x}~ , it is guaranteed that ~x~ is not divisible by ~998244353~ .

Here, there is a unique integer ~z~ between ~0~ and ~998244352~ such that ~xz \equiv y \pmod{998244353}~ . Print this ~z~ .

Constraints

• ~M \leq N \leq 1000~
• ~1 \leq M \leq 10~
• ~1 \leq K \leq 1000~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~ ~M~ ~K~

Output

Print the answer.

Sample Input 1

2 2 1

Sample Output 1

499122177

Takahashi wins in one spin if the wheel shows ~2~ . Therefore, the probability of winning is ~\frac{1}{2}~ .

We have ~2\times 499122177 \equiv 1 \pmod{998244353}~ , so the answer to be printed is ~499122177~ .

Sample Input 2

10 5 6

Sample Output 2

184124175

Sample Input 3

100 1 99

Sample Output 3

0