You are in a dungeon with five doors. In the dungeon there are two dungeon keepers, who are both either a liar or a knight. You know there is one liar and one knight. One door leads out of the dungeon, the other to certain death.

The keepers then tell you the following information:
Keeper A: If you asked me what door to take, there is no chance I would say E. If you asked the other keeper what door to take, he might say B.

Keeper B: If you asked me what door to take, there is no chance I would say C. If you asked the other keeper what door to take, he might say A.

Which door is the correct one?