Infectious Disease

In the year 2202, a strange disease begins to spread in a city of $n$ people. To stop the spread, experts invented a strong vaccine called Mysterious Oscar. On day $0$, one citizen is infected and another citizen is vaccinated. A vaccinated person is cured immediately and can neither catch nor spread the disease. On each later day $d$ ($d>0$), every citizen who was infected strictly before day $d$ chooses one uninfected and unvaccinated citizen with equal probability and infects that citizen. If an infected citizen has no uninfected and unvaccinated citizen left to choose, that citizen does nothing. After the infection step, every citizen who was vaccinated strictly before day $d$ chooses 2 different unvaccinated citizens with equal probability and persuades them to take the vaccine, one by one. If a vaccinated citizen has fewer than 2 unvaccinated citizens to choose from, that citizen persuades all the remaining unvaccinated citizens. Grammy wants to know how many days pass before the disease is fully extinguished. Find the expected number of days until all patients are cured.

It can be shown that the answer is an irreducible fraction $\frac{x}{y}$, where $x$ and $y$ are integers and $y \not\equiv 0 \pmod{10^9+7}$. Output the integer $x\cdot y^{-1}\pmod{10^9+7}$. In other words, output the integer $a$ with $0\leq a<10^9+7$ and $a\cdot y\equiv x\pmod{10^9+7}$.

The only line contains an integer $n$ ($2 \leq n \leq 1.4 \cdot 10^7$), the population of the city.

Output a single integer, the expected number of days before all patients are cured, modulo $10^9+7$.