--description--

We wish to tile a rectangle whose length is twice its width.

Let $T(0)$ be the tiling consisting of a single rectangle.

For $n > 0$, let $T(n)$ be obtained from $T( n- 1)$ by replacing all tiles in the following manner:

The following animation demonstrates the tilings $T(n)$ for $n$ from 0 to 5:

Let $f(n)$ be the number of points where four tiles meet in $T(n)$. For example, $f(1) = 0$, $f(4) = 82$ and $f({10}^9)\bmod {17}^7 = 126\,897\,180$.

Find $f({10}^k)$ for $k = {10}^{18}$, give your answer modulo ${17}^7$.

--hints--

rectangularTiling() should return 237696125.

assert.strictEqual(rectangularTiling(), 237696125);

--seed--

--seed-contents--

function rectangularTiling() {

  return true;
}

rectangularTiling();

--solutions--

// solution required