[ICPC 2018 Qingdao R] Plants vs. Zombies

Luogu

IDLGP9889

Time1000ms

Memory256MB

DifficultyP4

贪心2018二分O2优化ICPC青岛

BaoBao and DreamGrid are playing the game $\textit{Plants vs. Zombies}$. In the game, DreamGrid grows plants to defend his garden against BaoBao's zombies. ![](https://cdn.luogu.com.cn/upload/image_hosting/9tyl9ix3.png) $\textit{Plants vs. Zombies(?)} \\ \textit{(Image from pixiv. ID: 21790160; Artist: socha)}$ There are $n$ plants in DreamGrid's garden arranged in a line. From west to east, the plants are numbered from 1 to $n$ and the $i$-th plant lies $i$ meters to the east of DreamGrid's house. The $i$-th plant has a defense value of $d_i$ and a growth speed of $a_i$. Initially, $d_i = 0$ for all $1 \le i \le n$. DreamGrid uses a robot to water the plants. The robot is in his house initially. In one step of watering, DreamGrid will choose a direction (east or west) and the robot moves exactly 1 meter along the direction. After moving, if the $i$-th plant is at the robot's position, the robot will water the plant and $a_i$ will be added to $d_i$. Because the water in the robot is limited, at most $m$ steps can be done. The defense value of the garden is defined as $\min\{d_i | 1 \le i \le n\}$. DreamGrid needs your help to maximize the garden's defense value and win the game. - Each time the robot MUST move before watering a plant; - It's OK for the robot to move more than $n$ meters to the east away from the house, or move back into the house, or even move to the west of the house. ## Input There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains two integers $n$ and $m$ ($2 \le n \le 10^5$, $0 \le m \le 10^{12}$), indicating the number of plants and the maximum number of steps the robot can take. The second line contains $n$ integers $a_1, a_2, ... , a_n$ ($1 \le a_i \le 10^5$), where $a_i$ indicates the growth speed of the $i$-th plant. It's guaranteed that the sum of $n$ in all test cases will not exceed $10^6$. ## Output For each test case output one line containing one integer, indicating the maximum defense value of the garden DreamGrid can get. [samples] ## Note In the explanation below, `E` indicates that the robot moves exactly 1 meter to the east from his current position, and `W` indicates that the robot moves exactly 1 meter to the west from his current position. For the first test case, a candidate direction sequence is $\{E, E, W, E, E, W, E, E\}$, so that we have $d = \{6,6,12,6\}$ after the watering. For the second test case, a candidate direction sequence is $\{E, E, E, E, W, E, W, E, W\}$, so that we have $d = \{10, 10, 4\}$ after the watering.

Samples

Input #1

Output #1

6
4

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2018 Qingdao R] Plants vs. Zombies",
    "description": {
      "content": "BaoBao and DreamGrid are playing the game $\\textit{Plants vs. Zombies}$. In the game, DreamGrid grows plants to defend his garden against BaoBao's zombies. ![](https://cdn.luogu.com.cn/upload/image_h",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": {
      "LuoguStyle": "P4"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9889"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "BaoBao and DreamGrid are playing the game $\\textit{Plants vs. Zombies}$. In the game, DreamGrid grows plants to defend his garden against BaoBao's zombies.\n\n![](https://cdn.luogu.com.cn/upload/image_h...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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