CF1616D Keep the Average High

You are given an array of integers $ a_1, a_2, \ldots, a_n $ and an integer $ x $ . You need to select the maximum number of elements in the array, such that for every subsegment $ a_l, a_{l + 1}, \ldots, a_r $ containing strictly more than one element $ (l < r) $ , either: - At least one element on this subsegment is not selected, or - $ a_l + a_{l+1} + \ldots + a_r \geq x \cdot (r - l + 1) $ .

The first line of input contains one integer $ t $ ( $ 1 \leq t \leq 10 $ ): the number of test cases. The descriptions of $ t $ test cases follow, three lines per test case. In the first line you are given one integer $ n $ ( $ 1 \leq n \leq 50\,000 $ ): the number of integers in the array. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -100\,000 \leq a_i \leq 100\,000 $ ). The third line contains one integer $ x $ ( $ -100\,000 \leq x \leq 100\,000 $ ).

For each test case, print one integer: the maximum number of elements that you can select.

In the first example, one valid way to select the elements is $ [\underline{1}, 2, \underline{3}, \underline{4}, \underline{5}] $ . All subsegments satisfy at least one of the criteria. For example, for the subsegment $ l = 1 $ , $ r = 2 $ we have that the element $ 2 $ is not selected, satisfying the first criterion. For the subsegment $ l = 3 $ , $ r = 5 $ we have $ 3 + 4 + 5 = 12 \ge 2 \cdot 3 $ , satisfying the second criterion. We can't select all elements, because in this case for $ l = 1 $ , $ r = 2 $ all elements are selected and we have $ a_1 + a_2 = 3 < 2 \cdot 2 $ . Thus, the maximum number of selected elements is $ 4 $ . In the second example, one valid solution is $ [\underline{2}, \underline{4}, 2, \underline{4}, \underline{2}, \underline{4}, 2, \underline{4}, \underline{2}, \underline{4}] $ . In the third example, one valid solution is $ [\underline{-10}, -5, \underline{-10}] $ . In the fourth example, one valid solution is $ [\underline{9}, \underline{9}, -3] $ .