You have n cards. Each card has two non-negative integers, ai and bi. There is a counter c indicating how many cards can be played. At the the beginning of the game, c 1. Every time you play a card, you get ai points and also get the opportunity to play bi additional cards. Specifically, every time you play a card, c-c-1 +bi (-1 for playing a card, +b, for the card you played). The game is over when c 0 or all cards have been played. Design a greedy algorithm to find the maximum possible points you can get, and prove the correctness of your algorithm. Hint: one of the two following problems can be solved using a greedy algorithm, the other cannot. Recall that greedy algorithms are faster than dynamic pro- gramming algorithms, so you should always try to solve with a greedy algorithm when possible