--description--

Let $R(M, N)$ be the number of lattice points ($x$, $y$) which satisfy $M \lt x \le N$, $M \lt y \le N$ and $\left\lfloor\frac{y^2}{x^2}\right\rfloor$ is odd.

We can verify that $R(0, 100) = 3\,019$ and $R(100, 10\,000) = 29\,750\,422$.

Find $R(2 \times {10}^6, {10}^9)$.

Note: $\lfloor x\rfloor$ represents the floor function.

--hints--

pencilsOfRays() should return 301450082318807040.

assert.strictEqual(pencilsOfRays(), 301450082318807040);

--seed--

--seed-contents--

function pencilsOfRays() {

  return true;
}

pencilsOfRays();

--solutions--

// solution required