Maximum Integer Partition Product

An integer partition of a number $n$ is a way of writing $n$ as a sum of positive integers.

Partitions that differ only in the order of their summands are considered the same. A partition of $n$ into distinct parts is a partition of $n$ in which every part occurs at most once.

The partitions of $5$ into distinct parts are: $5, 4+1$ and $3+2$.

Let $f(n)$ be the maximum product of the parts of any such partition of $n$ into distinct parts and let $m(n)$ be the number of elements of any such partition of $n$ with that product.

So $f(5)=6$ and $m(5)=2$.

For $n=10$ the partition with the largest product is $10=2+3+5$, which gives $f(10)=30$ and $m(10)=3$. And their product, $f(10)·m(10) = 30·3 = 90$

It can be verified that $\sum f(n)\cdot m(n)$ for $1\le n \le 100 =1683550844462$.

Find $\sum f(n)\cdot m(n)$ for $1 \le n \le 10^{14}$. Give your answer modulo $982451653$, the $50$ millionth prime.