Ahimelech or Abiathar?

In 1 Samuel 21, David comes to Ahimelech the priest and asks for bread for himself and his men. However, in Mark 2, Jesus recounts the same details of the story, but states the time of Abiathar the high priest, not Ahimelech. This creates an unreconcilable contradiction in the Gospel narratives, either on the part of Mark in recording his Gospel or with Jesus in citing the incorrect priest from 1 Samuel 21.