First,I think it might use "Bit DP" to solve this problem.But I failed
    Second,I think it might have a method to make a solution for given N,M .But I can't find this method.
    Last,I want to calculate all the case because N and M is very small.But I can't decide whether it is the best solution for each case.
    I have no idea for this problem.Could you please tell me how to solve this problem?Thank you.
    By the way,I'm sorry for my poor English.I wish you could know what I say.