What is the mental element of a second-degree murder?

Although the statutory definition of first-degree murder includes "willful, deliberate, malicious, and premeditated killing," see 18 U.S.C. 1111(a), that definition does not extend to second-degree murder. See id. The mental element of second-degree murder is "malice aforethought." See United States v. Lesina, 833 F.2d at 158-59. Malice aforethought does not require an element of willfulness if the existence of that malice is inferred from the fact that defendant acted recklessly with extreme disregard for human life. Id. at 159. The district court properly set forth the alternatives in instructing that "with malice aforethought" means "either deliberately and intentionally or recklessly with extreme disregard for human life."