Derive the ideal soliton distribution. At the first iteration (t = 0) let the number of packets of degree d be h₀(d); show that (for d > 1) the expected number of packets of degree d that have their degree reduced to d - 1 is h0(d)d/K; and at the tth iteration, when t of the K packets have been recovered and the number of packets of degree d is ht(d), the expected number of packets of degree d that have their degree reduced to d - 1 is ht(d)d/(K - t). Hence show that in order to have the expected number of packets of degree 1 satisfy ht(1) = 1 for all t ∈ {0, . . . K - 1}, we must to start with have h₀(1) = 1 and h₀(2) = K/2; and more generally, ht(2) = (K - t)/2; then by recursion solve for h0(d) for d = 3 upwards.