CF1850E.Cardboard for Pictures

Mircea has $n$ pictures. The $i$-th picture is a square with a side length of $s_i$ centimeters.

He mounted each picture on a square piece of cardboard so that each picture has a border of $w$ centimeters of cardboard on all sides. In total, he used $c$ square centimeters of cardboard. Given the picture sizes and the value $c$, can you find the value of $w$?

A picture of the first test case. Here $c = 50 = 5^2 + 4^2 + 3^2$, so $w=1$ is the answer.

Please note that the piece of cardboard goes behind each picture, not just the border.

米尔恰有 $n$ 张照片。第 $i$ 张照片是一个边长为 $s_i$ 厘米的正方形。

他将每张照片粘贴在一个正方形纸板上，使得每张照片四周均有宽度为 $w$ 厘米的纸板边框。总共，他使用了 $c$ 平方厘米的纸板。已知各张照片的尺寸及总纸板面积 $c$，你能求出 $w$ 的值吗？

第一个测试用例的示意图。此处 $c = 50 = 5^2 + 4^2 + 3^2$，因此答案为 $w=1$。

请注意：纸板覆盖整张照片（即包含照片本身及其四周边框），而不仅限于边框部分。

The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.

The first line of each test case contains two positive integers $n$ ($1 \leq n \leq 2 \cdot 10^5$) and $c$ ($1 \leq c \leq 10^{18}$) — the number of paintings, and the amount of used square centimeters of cardboard.

The second line of each test case contains $n$ space-separated integers $s_i$ ($1 \leq s_i \leq 10^4$) — the sizes of the paintings.

The sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.

Additional constraint on the input: Such an integer $w$ exists for each test case.

Please note, that some of the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

第一行包含一个整数 $t$（$1 \leq t \leq 1000$）——测试用例的数量。

每个测试用例的第一行包含两个正整数 $n$（$1 \leq n \leq 2 \cdot 10^5$）和 $c$（$1 \leq c \leq 10^{18}$）——分别为画作的数量以及所用纸板的平方厘米总数。

每个测试用例的第二行包含 $n$ 个以空格分隔的整数 $s_i$（$1 \leq s_i \leq 10^4$）——表示各幅画作的尺寸。

所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

输入的额外约束：对每个测试用例，均存在满足条件的整数 $w$。

请注意，某些测试用例的部分输入可能超出 32 位整数类型的表示范围，因此在编程语言中应至少使用 64 位整数类型（例如 C++ 中的 long long）。

For each test case, output a single integer — the value of $w$ ($w \geq 1$) which was used to use exactly $c$ squared centimeters of cardboard.

对于每个测试用例，输出一个整数 —— 即恰好使用 $c$ 平方厘米纸板时所用的 $w$ 值（$w \geq 1$）。

The first test case is explained in the statement.

For the second test case, the chosen $w$ was $2$, thus the only cardboard covers an area of $c = (2 \cdot 2 + 6)^2 = 10^2 = 100$ squared centimeters.

For the third test case, the chosen $w$ was $4$, which obtains the covered area $c = (2 \cdot 4 + 2)^2 \times 5 = 10^2 \times 5 = 100 \times 5 = 500$ squared centimeters.

第一个测试用例已在题目描述中说明。

对于第二个测试用例，所选的 $w$ 为 $2$，因此唯一一张纸板覆盖的面积为 $c = (2 \cdot 2 + 6)^2 = 10^2 = 100$ 平方厘米。

对于第三个测试用例，所选的 $w$ 为 $4$，此时覆盖的面积为 $c = (2 \cdot 4 + 2)^2 \times 5 = 10^2 \times 5 = 100 \times 5 = 500$ 平方厘米。