Polynomial inequality?

Let $a_1$ , $a_2$ , ... $a_n$ , $k$ , and $M$ be positive integers such that $\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}=k\quad\text{and}\quad a_1a_2\cdots a_n=M$ If $M>1$ , and $P(x)=M(x+1)^k-(x+a_1)(x+a_2)\cdots (x+a_n)$ , then which of the following is true