CWMO 2018 Problem 4

In acute angled $\triangle ABC$ , $AB > AC$ , points $E, F$ lie on $AC, AB$ respectively, satisfying $BF+CE = BC$ . Let $I_B, I_C$ be the excenters of $\triangle ABC$ opposite $B, C$ respectively, $EI_C, FI_B$ intersect at $T$ , and let $K$ be the midpoint of arc $BAC$ . Let $KT$ intersect the circumcircle of $\triangle ABC$ at $K,P$ . Show $T,F,P,E$ concyclic.