Description:
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.
Input Format:
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++).
Output Format:
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.
Note:
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.