According to the Kebra Nagast, how did Solomon and the Queen of Sheba come to have a son?

The Kebra Nagast tells it as a story of wisdom and a trick. The Queen of Ethiopia, named Makeda, hears of Solomon from her merchant Tamrin and travels to Jerusalem, where she stays six months and gives up the worship of the sun for the God of Israel. Before she leaves, Solomon invites her to a banquet and serves food that will make her thirsty. That night she makes him swear not to take her by force, and he makes her swear to take nothing from his house. When she wakes and reaches for a jar of water, he holds her to her oath, and she frees him from his. Solomon gives her his ring as a sign for any child. Nine months and five days after they part she bears a son, Bayna-Lehkem. At twenty-two he goes to Jerusalem, where Solomon recognises him by his likeness, fails to keep him as heir, and has him anointed king of Ethiopia under the name David.