F. AmShZ Farm
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$998244353$$$.

Examples
Input
1 1
Output
1
Input
2 2
Output
8
Input
5 4
Output
50400
Input
20 100
Output
807645526
Input
10000000 10000
Output
883232350
Note

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