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 $a$.