--description--

On the parabola $y = \frac{x^2}{k}$, three points $A(a, \frac{a^2}{k})$, $B(b, \frac{b^2}{k})$ and $C(c, \frac{c^2}{k})$ are chosen.

Let $F(K, X)$ be the number of the integer quadruplets $(k, a, b, c)$ such that at least one angle of the triangle $ABC$ is 45°, with $1 ≤ k ≤ K$ and $-X ≤ a < b < c ≤ X$.

For example, $F(1, 10) = 41$ and $F(10, 100) = 12\,492$.

Find $F({10}^6, {10}^9)$.

--hints--

triangleOnParabola() should return 141630459461893730.

assert.strictEqual(triangleOnParabola(), 141630459461893730);

--seed--

--seed-contents--

function triangleOnParabola() {

  return true;
}

triangleOnParabola();

--solutions--

// solution required