{"raw_statement":[{"iden":"statement","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_hosting/9tyl9ix3.png)\n\n$\\textit{Plants vs. Zombies(?)} \\\\\n\\textit{(Image from pixiv. ID: 21790160; Artist: socha)}$\n\nThere 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 $1 \\le i \\le n$. \n\nDreamGrid 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.\n\nThe 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.\n\n- Each time the robot MUST move before watering a plant;\n- 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."},{"iden":"input","content":"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:\n\nThe 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.\n\nThe 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.\n\nIt's guaranteed that the sum of $n$ in all test cases will not exceed $10^6$."},{"iden":"output","content":"For each test case output one line containing one integer, indicating the maximum defense value of the garden DreamGrid can get."},{"iden":"note","content":"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.\n\nFor 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.\n\nFor 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."}],"translated_statement":null,"sample_group":[["2\n4 8\n3 2 6 6\n3 9\n10 10 1","6\n4"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}