--description--

You are given a pizza (perfect circle) that has been cut into $m·n$ equal pieces and you want to have exactly one topping on each slice.

Let $f(m,n)$ denote the number of ways you can have toppings on the pizza with $m$ different toppings ($m ≥ 2$), using each topping on exactly $n$ slices ($n ≥ 1$). Reflections are considered distinct, rotations are not.

Thus, for instance, $f(2,1) = 1$, $f(2,2) = f(3,1) = 2$ and $f(3,2) = 16$. $f(3,2)$ is shown below:

Find the sum of all $f(m,n)$ such that $f(m,n) ≤ {10}^{15}$.

--hints--

pizzaToppings() should return 1485776387445623.

assert.strictEqual(pizzaToppings(), 1485776387445623);

--seed--

--seed-contents--

function pizzaToppings() {

  return true;
}

pizzaToppings();

--solutions--

// solution required