You are given two sequences: `a0,...,an`

and `b0,...,bm`

Compute sequence `c0,…,c[n+m]`

such that
$c[i]=a[0]b[i]+a[1]b[i−1]+ \dots +a[i−1]b[1]+a[i]b[0]$

This is exactly what I needed here, where $a[i]= \binom{n}{i}$ and $b[i]= \binom{m}{i}$.
If I thought for a little longer I would realize that $c[i]=\binom{n+m}{i}$
instead of computing it using FFT.
#### § References

- [Codeforces contest comment by Swistakk) [https://codeforces.com/blog/entry/85348?#comment-730898 ]