Let $P(x)$ be a polynomial such that when $P(x)$ is divided by $x-19$, the remainder is 99 , and when $P(x)$ is divided by $x-99$, the remainder is 19. What is the remainder when $P(x)$ is divided by $(x-19)(x-99)$? (1999 AHSME Problems, Question \#17) 
选项为:A:$-x+80$  B:$x+80$  C:$-x+118$  D:$x+118$  E:$$0$$  请回答其中一个选项.