Avi and an A-mazeing Problem!

Avi is trapped in a maze. While walking, he is able to find some lost keys(all different). Assume that he picks up all and there are n keys with him. After a long and weary "journey", he is able to reach the exit. But, alas! The exit door has m locks on it and will open if and only if all locks are opened. But to open it, he has to give exactly m keys to a toy elf, who will, in turn try out all p