The poisoned brownie in the corner
Asked at Jane Street, Optiver
A tray holds a 5 by 7 grid of brownies. The brownie in the bottom-left corner is poisoned. On your turn you pick any remaining brownie and eat it together with every brownie above it and to its right (the whole rectangular block up-and-to-the-right of your choice). Players alternate; whoever is forced to eat the poisoned corner brownie loses.
Does the first player have a winning strategy? You don't need to describe the moves, just prove who wins.