OMCC 2020 Problem 5

Let $P(x)$ be a polynomial with real non-negative coefficients. Let $k$ be a positive integer and $x_1, x_2, \dots, x_k$ positive real numbers such that $x_1x_2\cdots x_k=1$ . Prove that $$P(x_1)+P(x_2)+\cdots+P(x_k)\geq kP(1).$$