# Problem 430: Range flips
N disks are placed in a row, indexed 1 to N from left to right. Each
disk has a black side and white side. Initially all disks show their
white side. At each turn, two, not necessarily distinct, integers A and
B between 1 and N (inclusive) are chosen uniformly at random. All disks
with an index from A to B (inclusive) are flipped. The following example
shows the case N = 8. At the first turn A = 5 and B = 2, and at the
second turn A = 4 and B = 6. Let E(N, M) be the expected number of disks
that show their white side after M turns. We can verify that E(3, 1) =
10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893. Find
E(1010, 4000). Give your answer rounded to 2 decimal places behind the
decimal point.