--description--

Inside a rope of length $n$, $n - 1$ points are placed with distance 1 from each other and from the endpoints. Among these points, we choose $m - 1$ points at random and cut the rope at these points to create $m$ segments.

Let $E(n, m)$ be the expected length of the second-shortest segment. For example, $E(3, 2) = 2$ and $E(8, 3) = \frac{16}{7}$. Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.

Find $E({10}^7, 100)$. Give your answer rounded to 5 decimal places behind the decimal point.

--hints--

cuttingRope() should return 2010.59096.

assert.strictEqual(cuttingRope(), 2010.59096);

--seed--

--seed-contents--

function cuttingRope() {

  return true;
}

cuttingRope();

--solutions--

// solution required