CF1027E.Inverse Coloring

You are given a square board, consisting of $n$ rows and $n$ columns. Each tile in it should be colored either white or black.

Let's call some coloring beautiful if each pair of adjacent rows are either the same or different in every position. The same condition should be held for the columns as well.

Let's call some coloring suitable if it is beautiful and there is no rectangle of the single color, consisting of at least $k$ tiles.

Your task is to count the number of suitable colorings of the board of the given size.

Since the answer can be very large, print it modulo $998244353$.

你被给定一个 $n$ 行 $n$ 列的方阵。其中每个格子需被染成白色或黑色。

我们称一种染色方案是优美的，当且仅当任意两个相邻的行在每个位置上要么完全相同，要么完全相反；列也需满足同样的条件。

我们称一种染色方案是合适的，当且仅当它既是优美的，且不存在由同一种颜色构成、且包含至少 $k$ 个格子的矩形。

你的任务是计算给定尺寸的方阵中合适的染色方案数。

由于答案可能非常大，请对 $998244353$ 取模后输出。

A single line contains two integers $n$ and $k$ ($1 \le n \le 500$, $1 \le k \le n^2$) — the number of rows and columns of the board and the maximum number of tiles inside the rectangle of the single color, respectively.

一行包含两个整数 $n$ 和 $k$（$1 \le n \le 500$，$1 \le k \le n^2$）—— 分别表示棋盘的行数与列数，以及单色矩形区域内最多可包含的方块数量。

Print a single integer — the number of suitable colorings of the board of the given size modulo $998244353$.

输出一个整数——给定尺寸棋盘的合适染色方案数对 $998244353$ 取模的结果。

Board of size $1 \times 1$ is either a single black tile or a single white tile. Both of them include a rectangle of a single color, consisting of $1$ tile.

Here are the beautiful colorings of a board of size $2 \times 2$ that don't include rectangles of a single color, consisting of at least $3$ tiles:

The rest of beautiful colorings of a board of size $2 \times 2$ are the following:

$1 \times 1$ 的棋盘要么由一块黑色方砖构成，要么由一块白色方砖构成。这两种情况均包含一个单色矩形，该矩形由 $1$ 块方砖组成。

以下为 $2 \times 2$ 棋盘的所有“优美着色”方案，其中不包含由至少 $3$ 块同色方砖组成的单色矩形：

其余的 $2 \times 2$ 棋盘的“优美着色”方案如下：