Let $f(a, b)$ denote the sum of divisors of $ab + 1$ which lies in the range $(a, b)$.

For example, $f(3, 23) = 5 + 7 + 10 + 14 = 36$.

Calculate $\sum_{i=1}^{p - 1}f(i, p)$ for $p = 1000000007$.