# [ICPC2018 Qingdao R] Plants vs. Zombies

## 题目描述

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.

## 输入输出格式

### 输入格式

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 $10^6$.

### 输出格式

For each test case output one line containing one integer, indicating the maximum defense value of the garden DreamGrid can get.

## 输入输出样例

### 输入样例 #1

2
4 8
3 2 6 6
3 9
10 10 1

### 输出样例 #1

6
4

## 说明

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.