What does "son of thy handmaid" means in Psalm 86:16 and Wisdom 9:5?

King Solomon and King David identified themselves both as servant although King and more so, both of them said they are the "son of thy handmaid". Are the mothers of King Solomon and King David a handmaid? Both of the passages does not imply King David and King Solomon referred to their biological mother when they uttered to God saying "son of thy handmaid". Or this passage is related to Jesus also a King but came in the form of a servant and became the "son of thy handmaid". This time St. Luke gospel reveals what the "son of thy handmaid" means. The Blessed Virgin Mary gave a title to herself and it doesn't came from angel revelations but from Her own words, staing Her role as the Mother of all the elect not just Jesus Christ. >Mary said, Behold, "I am the handmaid of the Lord. .." (Luke 1:38) Is King David and King Solomon prophesying the future role of Mary's name as a powerful intercessor and mediatrix of graces before the Throne of God?