Chain falling off a table-Lagrange Method

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Chain falling off a table--Lagrange Method

Chain of length L and mass M with uniform linear mass density slides off a frictionless table with dimensions L x L x L. Find the Lagrangian that describes this system. Then find the time when the last length leaves the table top.

I'm thoroughly confused on this question. Any hints to help me start?
 
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Some hints to get you started: What are the generalized coordinates (and how many are there)? To calculate the Lagrangian, you will find it useful to break the chain up into two parts.
 
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