write a go solution for Description:
There is a beautiful alley with trees in front of a shopping mall. Unfortunately, it has to go to make space for the parking lot.

The trees on the alley all grow in a single line. There are n spots for trees, index 0 is the shopping mall, index n+1 is the road and indices from 1 to n are the spots for trees. Some of them are taken — there grow trees of the same height k. No more than one tree grows in each spot.

When you chop down a tree in the spot x, you can make it fall either left or right. If it falls to the left, it takes up spots from x-k to x, inclusive. If it falls to the right, it takes up spots from x to x+k, inclusive.

Let m trees on the alley grow in some spots x_1,x_2,...,x_m. Let an alley be called unfortunate if all m trees can be chopped down in such a way that:

- no tree falls on the shopping mall or the road;
- each spot is taken up by no more than one fallen tree.

Calculate the number of different unfortunate alleys with m trees of height k. Two alleys are considered different if there is a spot y such that a tree grows in y on the first alley and doesn't grow in y on the second alley.

Output the number modulo 998,244,353.

Input Format:
The only line contains three integers n,m and k (1<=m,k<=n<=3*10^5) — the number of spots for the trees, the number of trees and the height of each tree.

Output Format:
Print a single integer — the number of different unfortunate alleys with m trees of height k, modulo 998,244,353.

Note:
None. Output only the code with no comments, explanation, or additional text.