# Problem 409: Nim Extreme

![graphic](img409.gif)

Let n be a positive integer. Consider nim positions where:There are n
non-empty piles. Each pile has size less than 2n. 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) =
19764360 and W(100) mod 1 000 000 007 = 384777056. Find W(10 000 000)
mod 1 000 000 007.