CF1528F.AmShZ Farm

To AmShZ, all arrays are equal, but some arrays are more-equal than others. Specifically, the arrays consisting of $n$ elements from $1$ to $n$ that can be turned into permutations of numbers from $1$ to $n$ by adding a non-negative integer to each element.

Mashtali who wants to appear in every problem statement thinks that an array $b$ consisting of $k$ elements is compatible with a more-equal array $a$ consisting of $n$ elements if for each $1 \le i \le k$ we have $1 \le b_i \le n$ and also $a_{b_1} = a_{b_2} = \ldots = a_{b_k}$.

Find the number of pairs of arrays $a$ and $b$ such that $a$ is a more-equal array consisting of $n$ elements and $b$ is an array compatible with $a$ consisting of $k$ elements modulo $998244353$.

Note that the elements of $b$ are not necessarily distinct, same holds for $a$.

对 AmShZ 而言，所有数组都是相等的，但有些数组比其他数组“更相等”。具体来说，“更相等”的数组是指：由 $1$ 到 $n$ 中的 $n$ 个元素组成的数组，且可通过给每个元素加上某个非负整数，将其变为 $1$ 到 $n$ 的一个排列。

Mashtali 希望在每道题的题面中都露脸，他定义：若数组 $b$（含 $k$ 个元素）满足对每个 $1 \le i \le k$ 都有 $1 \le b_i \le n$，且 $a_{b_1} = a_{b_2} = \ldots = a_{b_k}$，则称 $b$ 与“更相等”数组 $a$（含 $n$ 个元素）兼容。

求满足如下条件的数组对 $(a, b)$ 的个数（对 $998244353$ 取模）：

• $a$ 是一个含 $n$ 个元素的“更相等”数组；
• $b$ 是一个与 $a$ 兼容的、含 $k$ 个元素的数组。

注意：$b$ 的元素不一定互异，$a$ 的元素同样不一定互异。

The first line of input contains two integers $n$ and $k$ $(1 \le n \le 10^9 , 1 \le k \le 10^5)$.

输入的第一行包含两个整数 $n$ 和 $k$ $(1 \le n \le 10^9 , 1 \le k \le 10^5)$。

Print a single integer — the answer to the problem modulo $998244353$.

输出一个整数——该问题答案对 $998244353$ 取模的结果。

There are eight possible pairs for the second example:

1. $a = {1, 1}, b = {1, 1}$
2. $a = {1, 1}, b = {1, 2}$
3. $a = {1, 1}, b = {2, 1}$
4. $a = {1, 1}, b = {2, 2}$
5. $a = {1, 2}, b = {1, 1}$
6. $a = {1, 2}, b = {2, 2}$
7. $a = {2, 1}, b = {1, 1}$
8. $a = {2, 1}, b = {2, 2}$

第二个示例共有八种可能的数对：

1. $a = {1, 1}, b = {1, 1}$
2. $a = {1, 1}, b = {1, 2}$
3. $a = {1, 1}, b = {2, 1}$
4. $a = {1, 1}, b = {2, 2}$
5. $a = {1, 2}, b = {1, 1}$
6. $a = {1, 2}, b = {2, 2}$
7. $a = {2, 1}, b = {1, 1}$
8. $a = {2, 1}, b = {2, 2}$