JBMO-SL 2002 Problem 1

A student is playing computer. Computer shows randomly 2002 positive numbers. Game's rules let do the following operations

• to take 2 numbers from these, to double first one, to add the second one and to save the sum.
• to take another 2 numbers from the remainder numbers, to double the first one, to add the second one, to multiply this sum with previous and to save the result.
• to repeat this procedure, until all the 2002 numbers won't be used. Student wins the game if final product is maximum possible. Find the winning strategy and prove it.