Let $f(r,n)$ be the number of co-efficient which appears only once in expansion of (x₁+x₂+...+x_r)$^n$

then, $f(3,2) = 0$ and $f(3,3) = 1$

Let $A(i) = \sum_{j=1}^{n} f(i,j)$

and $B = \sum_{i=1}^{n} A(i)$

Find the value of $B$ $modulo$ $m$ if $n$=1000000000000 ($10^{12}$) and $m$=998244353.