CF1866H.Happy Sets

Define a set $A$ as a child of set $B$ if and only if for each element of value $x$ that is in $A$, there exists an element of value $x+1$ that is in $B$.

Given integers $N$ and $K$. In order to make Chaneka happy, you must find the number of different arrays containing $N$ sets $[S_1, S_2, S_3, \ldots, S_N]$ such that: - Each set can only contain zero or more different integers from $1$ to $K$. - There exists a way to rearrange the order of the array of sets into $[S'_1, S'_2, S'_3, \ldots, S'_N]$ such that $S'_i$ is a child of $S'_{i+1}$ for each $1\leq i\leq N-1$.

Print the answer modulo $998\,244\,353$.

Two sets are considered different if and only if there is at least one value that only occurs in one of the two sets.

Two arrays of sets are considered different if and only if there is at least one index $i$ such that the sets at index $i$ in the two arrays are different.

定义集合 $A$ 是集合 $B$ 的子集（child），当且仅当：对任意元素 $x \in A$，均有 $x+1 \in B$。

给定整数 $N$ 和 $K$。为使 Chaneka 开心，你需要计算满足以下条件的、由 $N$ 个集合组成的数组 $[S_1, S_2, S_3, \ldots, S_N]$ 的不同方案数：

• 每个集合 $S_i$ 只能包含 $1$ 到 $K$ 范围内的若干互不相同的整数（允许为空集）；
• 存在一种将该集合数组重排为 $[S'_1, S'_2, S'_3, \ldots, S'_N]$ 的方式，使得对每个 $1 \leq i \leq N-1$，均有 $S'_i$ 是 $S'_{i+1}$ 的子集（child）。

输出答案对 $998\,244\,353$ 取模的结果。

两个集合被视为不同，当且仅当存在至少一个整数，它仅属于其中某一个集合。

两个集合数组被视为不同，当且仅当存在至少一个下标 $i$，使得这两个数组在第 $i$ 个位置上的集合不同。

The only line contains two integers $N$ and $K$ ($1 \leq N,K \leq 2\cdot10^5$) — the number of sets in the array and the maximum limit for the values in the sets.

唯一一行包含两个整数 $N$ 和 $K$（$1 \leq N,K \leq 2\cdot10^5$）—— 分别表示数组中集合的数量以及集合中元素值的最大限制。

An integer representing the number of different arrays of sets that satisfy the problem condition, modulo $998\,244\,353$.

一个整数，表示满足题目条件的不同集合数组的个数，对 $998\,244\,353$ 取模。

In the first example, there are $11$ different arrays of sets possible, which are:

• $[{}, {}]$
• $[{}, {1}]$
• $[{}, {1, 2}]$
• $[{}, {2}]$
• $[{1}, {}]$
• $[{1}, {1, 2}]$
• $[{1}, {2}]$
• $[{1, 2}, {}]$
• $[{1, 2}, {1}]$
• $[{2}, {}]$
• $[{2}, {1}]$

在第一个例子中，共有 $11$ 种不同的集合数组，它们是：

• $[{}, {}]$
• $[{}, {1}]$
• $[{}, {1, 2}]$
• $[{}, {2}]$
• $[{1}, {}]$
• $[{1}, {1, 2}]$
• $[{1}, {2}]$
• $[{1, 2}, {}]$
• $[{1, 2}, {1}]$
• $[{2}, {}]$
• $[{2}, {1}]$