CF1528F.AmShZ Farm

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题目描述

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 $a$ .

输入格式

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

输出格式

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

输入输出样例

输入#1
```
1 1
```
输出#1
```
1
```
输入#2
```
2 2
```
输出#2
```
8
```
输入#3
```
5 4
```
输出#3
```
50400
```
输入#4
```
20 100
```
输出#4
```
807645526
```
输入#5
```
10000000 10000
```
输出#5
```
883232350
```

说明/提示

There are eight possible pairs for the second example:

$a = \{1, 1\}, b = \{1, 1\}$
$a = \{1, 1\}, b = \{1, 2\}$
$a = \{1, 1\}, b = \{2, 1\}$
$a = \{1, 1\}, b = \{2, 2\}$
$a = \{1, 2\}, b = \{1, 1\}$
$a = \{1, 2\}, b = \{2, 2\}$
$a = \{2, 1\}, b = \{1, 1\}$
$a = \{2, 1\}, b = \{2, 2\}$

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