--description--

$N$ 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 $E(3, 1) = \frac{10}{9}$, $E(3, 2) = \frac{5}{3}$, $E(10, 4) ≈ 5.157$ and $E(100, 10) ≈ 51.893$.

Find $E({10}^{10}, 4000)$. Give your answer rounded to 2 decimal places behind the decimal point.

--hints--

rangeFlips() should return 5000624921.38.

assert.strictEqual(rangeFlips(), 5000624921.38);

--seed--

--seed-contents--

function rangeFlips() {

  return true;
}

rangeFlips();

--solutions--

// solution required