Block matching pattern matching problem
If the numbers are all integers at most $k$, then you can apply a fast algorithm for substring matching with don't-care symbols (see below) to solve the problem in $O(kn(\log m + \log k))$ time by applying the following transformation:


Map each text character $t$ to $t-1$ zeros followed by a 1.
Map each pattern character $p$ to $p-1$ don't-care symbols followed by a 1, and also prepend a 1 to the overall pattern.


Basically, 1s represent "boundaries" in both strings, and we look for a way to make each boundary in the pattern line up with some boundary in the text.

This paper describes an $O(n+m+\alpha)$-time algorithm, where $\alpha$ is "the total number of occurrences of the subpatterns" (I didn't read the full paper, so I'm not sure exactly what that means).  In any case it mentions the 1974 algorithm of Fischer and Paterson, "String matching and other products", which solves the problem in $O(n\log m\log \Sigma)$ time -- though that link is behind a paywall, googling should find other information on it.