Be Efficient

Consider an integer sequence consisting of $n$ elements:

You are given $a$, $b$, $c$, $m$, and $n$. Find the number of consecutive subsequences whose sum is divisible by $m$.

For example, let a = 2, b = 1, c = 2, m = 4, n = 4. Then

So, x_0 = 2, x_1 = 1, x_2 = 4, x_3 = 3. The consecutive subsequences are $\{2\}$, $\{2,1\}$, \{2, 1, 4\}, \{2, 1, 4, 3\}, $\{1\}$, $\{1,4\}$, \{1, 4, 3\}, $\{4\}$, $\{4,3\}$, and $\{3\}$. Of these $10$ consecutive subsequences, only two have a sum divisible by $4$: \{1, 4, 3\} and $\{4\}$.