CF1574C Slay the Dragon

Recently, Petya learned about a new game "Slay the Dragon". As the name suggests, the player will have to fight with dragons. To defeat a dragon, you have to kill it and defend your castle. To do this, the player has a squad of $ n $ heroes, the strength of the $ i $ -th hero is equal to $ a_i $ . According to the rules of the game, exactly one hero should go kill the dragon, all the others will defend the castle. If the dragon's defense is equal to $ x $ , then you have to send a hero with a strength of at least $ x $ to kill it. If the dragon's attack power is $ y $ , then the total strength of the heroes defending the castle should be at least $ y $ . The player can increase the strength of any hero by $ 1 $ for one gold coin. This operation can be done any number of times. There are $ m $ dragons in the game, the $ i $ -th of them has defense equal to $ x_i $ and attack power equal to $ y_i $ . Petya was wondering what is the minimum number of coins he needs to spend to defeat the $ i $ -th dragon. Note that the task is solved independently for each dragon (improvements are not saved).

The first line contains a single integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — number of heroes. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^{12} $ ), where $ a_i $ is the strength of the $ i $ -th hero. The third line contains a single integer $ m $ ( $ 1 \le m \le 2 \cdot 10^5 $ ) — the number of dragons. The next $ m $ lines contain two integers each, $ x_i $ and $ y_i $ ( $ 1 \le x_i \le 10^{12}; 1 \le y_i \le 10^{18} $ ) — defense and attack power of the $ i $ -th dragon.

Print $ m $ lines, $ i $ -th of which contains a single integer — the minimum number of coins that should be spent to defeat the $ i $ -th dragon.

To defeat the first dragon, you can increase the strength of the third hero by $ 1 $ , then the strength of the heroes will be equal to $ [3, 6, 3, 3] $ . To kill the dragon, you can choose the first hero. To defeat the second dragon, you can increase the forces of the second and third heroes by $ 1 $ , then the strength of the heroes will be equal to $ [3, 7, 3, 3] $ . To kill the dragon, you can choose a second hero. To defeat the third dragon, you can increase the strength of all the heroes by $ 1 $ , then the strength of the heroes will be equal to $ [4, 7, 3, 4] $ . To kill the dragon, you can choose a fourth hero. To defeat the fourth dragon, you don't need to improve the heroes and choose a third hero to kill the dragon. To defeat the fifth dragon, you can increase the strength of the second hero by $ 2 $ , then the strength of the heroes will be equal to $ [3, 8, 2, 3] $ . To kill the dragon, you can choose a second hero.