Woodcutter

Milan the woodcutter has to bring home a certain amount of wood. His saw sits on a stand that can be set to any integer height in meters, and it cuts every tree in the forest at exactly that height. Only the part of a tree above the blade falls down - a tree that is not taller than the blade is left untouched.

The higher the saw stands, the less wood Milan gets. He cares about the forest, so he does not want to cut a single meter more than he needs.

All trunks are equally thick, so the amount of wood is simply measured in meters of cut trunk. Your task is to find the highest integer height at which Milan can set the saw and still get at least the amount of wood he needs.

Input

First line of input will be a single integer $t$ - the number of testcases.
The first line of each testcase contains two integers $n$ and $x$ - the number of trees in the forest and the amount of wood Milan needs.
The second line contains $n$ integers $h_1,h_2,\dots ,h_n$ - the heights of the trees.

Output

For every testcase print a single line with the highest height at which the saw can be set.

Example

2
5 14
24 21 19 14 22
1 7
7

18
0

In the first testcase the saw set to $18$ meters takes $6$ meters off the first tree, $3$ off the second, $1$ off the third, nothing off the fourth and $4$ off the fifth - exactly the $14$ meters Milan needs. In the second testcase the only tree has to be cut all the way to the ground.

Constraints

$1\le t\le 10$
$1\le n\le 10^5$
$1\le h_i\le 10^4$
$1\le x\le h_1+h_2+\cdots +h_n$ - there is always enough wood in the forest

This problem was adapted, with permission, from Drva, authored by Društvo matematičara Srbije and Fondacija Petlja.