I work in Engineering and my PhD students often do what you describe. In my opinion, you should be the first author.

• you have set the problem
• you have set the outline of the solution and supervised the student
• you have composed the paper

To allow the master student first authorship, they usually need to:

• contribute at least some novel ideas
• take most of the writing burden

I work in an engineering field, and my PhD students often do what you described. In my opinion, you should be the first author because

• you have set the problem;
• you have set the outline of the solution and supervised the student;
• you have composed the paper.

To grant the first authorship to a master student, she usually needs to

• at least contribute to the development some novel ideas;
• take most of the writing burden.