Does depraved heart murder, described as reckless disregard for human life, include wilfullness?

Expl: if the question says "a statute defines first degree murder as intentional and premeditated killing." You know first degree murder under the statute encompasses intentional murder under common law.

BUT, if the question says "a statute defines first degree murder as murder committed willfully and with intention and premeditation, does this mean first degree murder encompasses intentional murder AND depraved heart murder under common law?

A state statute divides murder into degrees and defines murder in the first degree as murder committed willfully with premeditation and deliberation. The statute defines murder in the second degree as all other murder at common law and defines voluntary manslaughter as at common law. A man hated one of his coworkers. Upon learning that the coworker was at a neighbor's house, the man grabbed his gun and went to the neighbor's house hoping to provoke the coworker into attacking him so that he could then shoot the coworker. After arriving at the house, the man insulted the coworker and bragged that he had had sexual relations with the coworker's wife two weeks earlier. This statement was not true, but it enraged the coworker, who grabbed a knife from the kitchen table and ran toward the man. The man then shot and killed the coworker. What is the most serious homicide offense of which the man could properly be convicted?