Let triangle △ABC have AB=17, BC=14, CA=12. Let MA, MB, MC be midpoints of BC, AC, and AB respectively. Let the angle bisectors of A, B, and C intersect BC, AC, and AB at P, Q, and R, respectively. Reflect MA about AP, MB about BQ, and MC about CR to obtain MA′, MB′, MC′, respectively. The lines AMA′, BMB′, and CMC′ will then intersect BC, AC, and AB at D, E, and F, respectively. Given that AD, BE, and CF concur at a point K inside the triangle, in simplest form, the ratio [KAB]:[KBC]:[KCA] can be written in the form p:q:r, where p, q and r are relatively prime positive integers and [XYZ] denotes the area of △XYZ. Compute p+q+r.