Now, consider the change problem in Binaryland. The input to this problem is an integer L. The output should be the minimum cardinality collection of coins required to make L cents of change (that is, you want to use as few coins as possible). In Binaryland, the coins are worth 1, 2, 22, 23, ..., 21000 cents. Assume that you have an unlimited number of coins of each type. Prove or disprove that the greedy algorithm (that takes as many coins of the highest value as possible) solves the change problem in Binaryland. HINT: The greedy algorithm is correct for one of the above two problems and is incorrect for the other.