AmShZ Farm

2000ms

262144K

Description:

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 $$$a$$$.

Input:

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

Output:

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

Sample Input:

1 1

Sample Output:

Sample Input:

2 2

Sample Output:

Sample Input:

5 4

Sample Output:

Sample Input:

20 100

Sample Output:

807645526

Sample Input:

10000000 10000

Sample Output:

883232350

Note:

There are eight possible pairs for the second example:

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

Informação

Provedor Codeforces

Código CF1528F