Can anyone tell how to solve BIPFAMIL

Hey guys!

I was trying to solve A Family of Bipartite Graphs from this years ICPC. I tried to go for a dp appraoch but sadly couldnt correctly frame the recurrence. Can anyone who has solved/upsolved it help me get the intuition for it? Curious because some people said its standard dp.

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i was just thinking that
this might be the correct formula but when i submitted it is showing wrong answer