Product of tuple

Let $S(p,n)$ denote the number of $n$-tuples of positive integers whose product is no larger than $p$. For example, $S(4,2)=8$, as there are eight 2-tuples (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (4, 1) meet the condition. You are also given $S(6,4)=39$, $S(10,10)=571$, $S(100,100)mod1000000007=959337187$.

Find $S({10}^{12},{10}^{12})mod1000000007$.

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Thanks to baihacker for the idea.

This problem was inspired by Problem 452 at Project Euler (https://projecteuler.net/problem=452)