Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

The college of computer & software is going to hold an ACM contest. N (0<N<=1000) students have registered for the contest, and the teacher LCY has thought up M (0<M<=15) problems numbered from 1 to M. LCY is so familiar with the students that he can forecast the result of every student for the M problems.

Now he will select as many problems as possible from the M problems. And he want at least K (0<=K<=M) students to solve all problems. Will you compute the maximum number of problems he can choose? Output "0" if there is no selection can satisfy the condition.

Now he will select as many problems as possible from the M problems. And he want at least K (0<=K<=M) students to solve all problems. Will you compute the maximum number of problems he can choose? Output "0" if there is no selection can satisfy the condition.

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