Number of Divisors

Let $d(n)$ be the number of divisors of a positive integer $n$.

Given three integers $a$, $b$, and $c$, write a program that computes the value of the following sum.

$\sum_{i=1}^{a}\sum_{j=1}^{b}\sum_{k=1}^{c} d(i \times j \times k)$

The first line contains $a$, $b$, and $c$, separated by spaces. ($1 \le a, b, c \le 2000$)

Print the value of the sum modulo $2^{30}$ on the first line. $2^{30}$ is 1073741824.