Question about broadcasting an ARP request

Hi, my course material doesn't seem to address this so I wanted to ask here. Say there are two hosts A and B on different subnetworks connected by a router. A wants to send to B and knows only B's IP. If A's ARP table is empty he would broadcast an ARP request, but assume instead that A has the IP and MAC of the router. Will A still broadcast? Or will A unicast to the router? I ask this because A should be able to derive that B is not on the same subnet by comparing NetIDs. Therefore should A recognize that sending the datagram only to the router makes sense.

Thanks!