Shopping in AtCoder store

AtCoder

IDabc289_g

Time2000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Takahashi runs AtCoder store. $N$ customers visit the store, and $M$ items are sold in the store. The motivation of the $i$\-th $(1\leq i\leq N)$ customer is $B _ i$. The value of the $j$\-th $(1\leq j\leq M)$ item is $C _ j$. Takahashi sets a price for each item. The $i$\-th customer buys one $j$\-th item if and only if its price $P _ j$ satisfies: * $B _ i+C _ j\geq P _ j$. For each $j=1,2,\ldots,M$, find the gross sale of the $j$\-th item when Takahashi sets the price so that the sale is maximized. The gross sale of the $j$\-th item is defined as the product of $P _ j$ and the number of customers that buys the $j$\-th item. ## Constraints * $1\leq N\leq2\times10^5$ * $1\leq M\leq2\times10^5$ * $0\leq B _ i\leq10^9\quad(1\leq i\leq N)$ * $0\leq C _ i\leq10^9\quad(1\leq i\leq M)$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $B _ 1$ $B _ 2$ $\ldots$ $B _ N$ $C _ 1$ $C _ 2$ $\ldots$ $C _ M$ [samples]

高桥经营一家AtCoder商店。有 $N$ 位顾客光顾该商店，商店中出售 $M$ 件商品。第 $i$ 位顾客（$1\leq i\leq N$）的购买动机为 $B _ i$。第 $j$ 件商品（$1\leq j\leq M$）的价值为 $C _ j$。高桥为每件商品设定价格。第 $i$ 位顾客会购买第 $j$ 件商品，当且仅当该商品的价格 $P _ j$ 满足： * $B _ i+C _ j\geq P _ j$。对于每个 $j=1,2,\ldots,M$，请找出当高桥将价格设定为使该商品销售额最大化时，第 $j$ 件商品的总销售额。第 $j$ 件商品的总销售额定义为价格 $P _ j$ 与购买该商品的顾客数量的乘积。 ## Constraints * $1\leq N\leq2\times10^5$ * $1\leq M\leq2\times10^5$ * $0\leq B _ i\leq10^9\quad(1\leq i\leq N)$ * $0\leq C _ i\leq10^9\quad(1\leq i\leq M)$ * 输入中的所有值均为整数。 ## Input 输入从标准输入按以下格式给出： $N$ $M$ $B _ 1$ $B _ 2$ $\ldots$ $B _ N$ $C _ 1$ $C _ 2$ $\ldots$ $C _ M$ [samples]

Samples

Input #1

5 4
100 200 300 400 500
120 370 470 80

Output #1

1280 2350 2850 1140

For example, he may set the price of the $1$\-st item to $320$; then the $2$\-nd, $3$\-rd, $4$\-th, and $5$\-th customers will buy one. The gross sale of the $1$\-st item will be $1280$. Since he cannot make the gross sale of the $1$\-st item greater than $1280$, the $1$\-st value to be printed is $1280$.

Input #2

4 4
0 2 10 2
13 13 0 4

Output #2

52 52 10 18

Two customers may have the same motivation. Also, two items may have the same value.

Input #3

12 15
16 592 222 983 729 338 747 61 451 815 838 281
406 319 305 519 317 590 507 946 365 5 673 478 340 176 2

Output #3

6280 5466 5382 7410 5454 8120 7290 11680 5870 3670 8950 7000 5620 4608 3655

Input #4

5 5
1000000000 1000000000 1000000000 1000000000 1000000000
1000000000 1000000000 1000000000 1000000000 1000000000

Output #4

10000000000 10000000000 10000000000 10000000000 10000000000

Note that the gross sales may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "Shopping in AtCoder store",
    "description": {
      "content": "Takahashi runs AtCoder store. $N$ customers visit the store, and $M$ items are sold in the store. The motivation of the $i$\\-th $(1\\leq i\\leq N)$ customer is $B _ i$. The value of the $j$\\-th $(1\\leq ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc289_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi runs AtCoder store. $N$ customers visit the store, and $M$ items are sold in the store. The motivation of the $i$\\-th $(1\\leq i\\leq N)$ customer is $B _ i$. The value of the $j$\\-th $(1\\leq ...",
      "is_translate": false,
      "language": "English"
    },
    {
      "statement_type": "Markdown",
      "content": "高桥经营一家AtCoder商店。有 $N$ 位顾客光顾该商店，商店中出售 $M$ 件商品。第 $i$ 位顾客（$1\\leq i\\leq N$）的购买动机为 $B _ i$。第 $j$ 件商品（$1\\leq j\\leq M$）的价值为 $C _ j$。\n高桥为每件商品设定价格。第 $i$ 位顾客会购买第 $j$ 件商品，当且仅当该商品的价格 $P _ j$ 满足：\n\n* $B _ i+C _ j\\g...",
      "is_translate": true,
      "language": "Chinese"
    }
  ]
}

Full JSON Raw Segments