Evaluation using Stokes theorem

Question

I have encountered a problem on Stokes theorem which is as follows:

Evaluate $$\int_C y \, dx + z \,dy + x \, dz $$ where C is the curve of intersection of $x^2+y^2+z^2=a^2$ and $x+z=a$

I am not sure of how to parametrize the curve.

Thanks in advance!!

Edit: My work

$$F=[y \, , z \, , x]$$

$$\nabla\times F= [-1,-1,-1] $$

How do I proceed with parametrisation of the given surfaces??