The girl with the sight (Death Note x OC)

Sayori Makato, a 17 year old homeschooled student transferring to highschool for her final year. Exceptional grades lands her in the top ten students of the grade. She has a rare gift, an ability to see the dead...and naturally, supernatural entities. She notices a figure looming over one of her classmates, and it's enough to peek her interest. During this time, an infamous killer is on the loose, somehow murdering criminals throughout Japan. Nicknamed Kira, coming from the English word Killer, Light Yagami tries to keep his cover under the watchful eye of L, a well known detective without an appearance. what happens when curiosity killed the cat, and the dog comes to investigate?