Boundary points of the set D={(x,y): |y |>= x}

Question

What are the boundary points of the set in xy-plane $$ D=\{(x,y): x^2+y^2<1, |y| \geqslant x\} $$

Should it be $bdry(D)=\{(x,y):x^2+y^2=1, |y|=x\}$ or $bdry(D)=\{(x,y):x^2+y^2=1, |y|\geqslant x\}$ ? That is the absolut value that I am not sure about.