1787C · Remove the Bracket

Problem: RSJ has a sequence $a$ of $n$ integers $a_1,a_2, \ldots, a_n$ and an integer $s$. For each of $a_2,a_3, \ldots, a_{n-1}$, he chose a pair of non-negative integers $x_i$ and $y_i$ such that $x_i+y_i=a_i$ and $(x_i-s) \cdot (y_i-s) \geq 0$.

Now he is interested in the value $F = a_1 \cdot x_2+y_2 \cdot x_3+y_3 \cdot x_4 + \ldots + y_{n - 2} \cdot x_{n-1}+y_{n-1} \cdot a_n.$

Please help him find the minimum possible value $F$ he can get by choosing $x_i$ and $y_i$ optimally. It can be shown that there is always at least one valid way to choose them.

Input Format: Each test contains multiple test cases. The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$, $s$ ($3 \le n \le 2 \cdot 10^5$; $0 \le s \le 2 \cdot 10^5$).

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0 \le a_i \le 2 \cdot 10^5$).

It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$.

Output Format: For each test case, print the minimum possible value of $F$.

Note: In the first test case, $2\cdot 0+0\cdot 1+0\cdot 3+0\cdot 4 = 0$.

In the second test case, $5\cdot 1+2\cdot 2+2\cdot 2+1\cdot 5 = 18$.