RU-SPB 2014 Problem 92

All angles of $ABC$ are in $(30,90)$ . Circumcenter of $ABC$ is $O$ and circumradius is $R$ . Point $K$ is projection of $O$ to angle bisector of $\angle B$ , point $M$ is midpoint $AC$ . It is known, that $2KM=R$ . Find $\angle B$