Different Summands Counting

Consider all ordered partitions of a positive integer $n$ into $m$ positive summands: $n = a\_1 + a\_2 + \ldots + a\_m$. Let $f(a\_1, a\_2, \ldots, a\_m)$ be the number of different integers among $a\_1, a\_2, \ldots, a\_m$. Find the sum of $f(a\_1, a\_2, \ldots, a\_m)$ over all ordered partitions of the number $n$, and print it modulo $998\\,244\\,353$.

Two ordered partitions $a\_1 + a\_2 + \ldots + a\_m = n$ and $b\_1 + b\_2 + \ldots + b\_m = n$ are considered different if there is an index $i \in \\{1, 2, \ldots, m\\}$ such that $a\_i \neq b\_i$.

The only line of input contains two integers $n$ and $m$ ($1 \le n \le 10^{18}$, $1 \le m \le 500$, $m \le n$).

Print the answer modulo $998\\,244\\,353$.