CF1787C Remove the Bracket

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.

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 $ .

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

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 $ .