--description--

A row measuring n units in length has red blocks with a minimum length of m units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one black square.

Let the fill-count function, $F(m, n)$, represent the number of ways that a row can be filled.

For example, $F(3, 29) = 673135$ and $F(3, 30) = 1089155$.

That is, for m = 3, it can be seen that n = 30 is the smallest value for which the fill-count function first exceeds one million.

In the same way, for m = 10, it can be verified that $F(10, 56) = 880711$ and $F(10, 57) = 1148904$, so n = 57 is the least value for which the fill-count function first exceeds one million.

For m = 50, find the least value of n for which the fill-count function first exceeds one million.

Note: This is a more difficult version of Problem 114.

--hints--

countingBlockTwo() should return 168.

assert.strictEqual(countingBlockTwo(), 168);

--seed--

--seed-contents--

function countingBlockTwo() {

  return true;
}

countingBlockTwo();

--solutions--

// solution required