freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-409-nim-extreme.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5061000cf542c510017	Problem 409: Nim Extreme	5	302077	problem-409-nim-extreme

--description--

Let n be a positive integer. Consider nim positions where:

• There are n non-empty piles.
• Each pile has size less than 2^n.
• No two piles have the same size.

Let W(n) be the number of winning nim positions satisfying the above conditions (a position is winning if the first player has a winning strategy).

For example, W(1) = 1, W(2) = 6, W(3) = 168, W(5) = 19\\,764\\,360 and W(100)\bmod 1\\,000\\,000\\,007 = 384\\,777\\,056.

Find W(10\\,000\\,000)\bmod 1\\,000\\,000\\,007.

--hints--

nimExtreme() should return 253223948.

assert.strictEqual(nimExtreme(), 253223948);

--seed--

--seed-contents--

function nimExtreme() {

  return true;
}

nimExtreme();

--solutions--

// solution required