Trader Problem

题意翻译

在交易系统中，你可以用一个价值为 $x$ 的物品换取一个价值不超过 $x+k$ 的物品（$k$ 为常数）。 给定你手中的 $n$ 个物品，以及系统的 $m$ 个物品分别的价值，有 $q$ 次询问，对于每次询问，给定 $k$，求经过若干次交易后你手上物品的总价值最大是多少。 **注：询问之间互相独立。** $1\le n,m,q\le2\times 10^5$ $ 0 \le k \le 10^9 $ 其他所有数据都在 $[1,10^9]$ 以内。

题目描述

Monocarp plays a computer game (yet again!). This game has a unique trading mechanics. To trade with a character, Monocarp has to choose one of the items he possesses and trade it for some item the other character possesses. Each item has an integer price. If Monocarp's chosen item has price $ x $ , then he can trade it for any item (exactly one item) with price not greater than $ x+k $ . Monocarp initially has $ n $ items, the price of the $ i $ -th item he has is $ a_i $ . The character Monocarp is trading with has $ m $ items, the price of the $ i $ -th item they have is $ b_i $ . Monocarp can trade with this character as many times as he wants (possibly even zero times), each time exchanging one of his items with one of the other character's items according to the aforementioned constraints. Note that if Monocarp gets some item during an exchange, he can trade it for another item (since now the item belongs to him), and vice versa: if Monocarp trades one of his items for another item, he can get his item back by trading something for it. You have to answer $ q $ queries. Each query consists of one integer, which is the value of $ k $ , and asks you to calculate the maximum possible total cost of items Monocarp can have after some sequence of trades, assuming that he can trade an item of cost $ x $ for an item of cost not greater than $ x+k $ during each trade. Note that the queries are independent: the trades do not actually occur, Monocarp only wants to calculate the maximum total cost he can get.

输入输出格式

输入格式

The first line contains three integers $ n $ , $ m $ and $ q $ ( $ 1 \le n, m, q \le 2 \cdot 10^5 $ ). The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the prices of the items Monocarp has. The third line contains $ m $ integers $ b_1, b_2, \dots, b_m $ ( $ 1 \le b_i \le 10^9 $ ) — the prices of the items the other character has. The fourth line contains $ q $ integers, where the $ i $ -th integer is the value of $ k $ for the $ i $ -th query ( $ 0 \le k \le 10^9 $ ).

输出格式

For each query, print one integer — the maximum possible total cost of items Monocarp can have after some sequence of trades, given the value of $ k $ from the query.

输入输出样例

输入样例 #1

3 4 5
10 30 15
12 31 14 18
0 1 2 3 4

输出样例 #1

55
56
60
64
64