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id	title	challengeType	forumTopicId	dashedName
5900f5081000cf542c51001a	Problem 412: Gnomon numbering	5	302081	problem-412-gnomon-numbering

--description--

For integers m, n (0 ≤ n < m), let L(m, n) be an m×m grid with the top-right n×n grid removed.

For example, L(5, 3) looks like this:

5x5 grid, with removed 3x3 grid from the top-right

We want to number each cell of L(m, n) with consecutive integers 1, 2, 3, ... such that the number in every cell is smaller than the number below it and to the left of it.

For example, here are two valid numberings of L(5, 3):

Let LC(m, n) be the number of valid numberings of L(m, n). It can be verified that LC(3, 0) = 42, LC(5, 3) = 250\\,250, LC(6, 3) = 406\\,029\\,023\\,400 and LC(10, 5)\bmod 76\\,543\\,217 = 61\\,251\\,715.

Find LC(10\\,000, 5\\,000)\bmod 76\\,543\\,217.

--hints--

gnomonNumbering() should return 38788800.

assert.strictEqual(gnomonNumbering(), 38788800);

--seed--

--seed-contents--

function gnomonNumbering() {

  return true;
}

gnomonNumbering();

--solutions--

// solution required

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