Basing My Film Off a Stephen King Story

I believe that basing my film off a short story will be a good idea for this project as I will be able to focus my time in writing a decent screenplay, rather than worrying about creating a cohesive and well paced story. As I am looking to make a horror/thriller for my project, Stephen King offers some off the best stories and it would be stupid of me not to look into them at all. A number of his stories have already been made into successful films such as "The Shinning", "The Green Mile" and "The Shawshank Redemption". This shows me that his stories can be adapted well and all I need to now is find one that suits what I am after.