--description--

Let's call a lattice point ($x$, $y$) inadmissible if $x$, $y$ and $x + y$ are all positive perfect squares.

For example, (9, 16) is inadmissible, while (0, 4), (3, 1) and (9, 4) are not.

Consider a path from point ($x_1$, $y_1$) to point ($x_2$, $y_2$) using only unit steps north or east. Let's call such a path admissible if none of its intermediate points are inadmissible.

Let $P(n)$ be the number of admissible paths from (0, 0) to ($n$, $n$). It can be verified that $P(5) = 252$, $P(16) = 596\,994\,440$ and $P(1\,000)\bmod 1\,000\,000\,007 = 341\,920\,854$.

Find $P(10\,000\,000)\bmod 1\,000\,000\,007$.

--hints--

admissiblePaths() should return 299742733.

assert.strictEqual(admissiblePaths(), 299742733);

--seed--

--seed-contents--

function admissiblePaths() {

  return true;
}

admissiblePaths();

--solutions--

// solution required