It is known that $ k$ and $ n$ are positive integers and [ k + 1\leq\sqrt {\frac {n + 1}{\ln(n + 1)}}.] Prove that there exists a polynomial $ P(x)$ of degree $ n$ with coefficients in the set $ \{0,1, - 1\}$ such that $ (x - 1)^{k}$ divides $ P(x)$.