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