I need to know if a Circut or Part exists

Hello All, I'm building a two man authorization box for model rocketry, the reason for this is actually a funny and long story with a very painful (minor burns) but still funny end.

I have devised most of the circutry, simple buttons and relays of course, but I cant figure out how to create the key lockout circut. I need a circut that meets the following requirements:

• 
  If Input A is High then Set Output High
  If Input B is High and Input A is High Set Output High
  If Input B is High and Input A goes Low Set Output Low and lock Input A out
  If Input A is Low and Input B goes High set Output low and Lock out A

Basically What this circut does is decides if the key has been turned before a timer circut brings the other input high. using 2 of these circuits(one for each Key) when Man 1 turns his key it brings input A on circuit 1 high and activates a 555 timer IC which counts off approx 750ms and then brings Input B high on circuit 1 and 2 thus giving an aprox 3/4ths of a second delay if the keys are not turned in 100% perfect timing but locks out launch if either the keys arnt turned together or one key is turned off.

Is there a chip that can do this, or can someone show me a schematic of a circuit that can do this? I have circuits I designed which i think are close but each design fails in someway to meet all my requirements.

what is meant by "and lock Input A out " , locking the ckts o/p so that any i/p wont affect the o/p until a reset is done ?

Not Quite, What I mean is I want it so that If Input A is Low when Input B High then I want it to ignore input A from that point on(untill a reset is done). Pretty much I want The output to Mimic A but only as long as B is low. with the exception of A changing from High tolow, then I want the output to go Low.

You are close but I want Input A to Only alow a Change from High to Low, Once Input B is High The circut would ignore Input A if it changed from Low to High