CF1704B Luke is a Foodie

Luke likes to eat. There are $ n $ piles of food aligned in a straight line in front of him. The $ i $ -th pile contains $ a_i $ units of food. Luke will walk from the $ 1 $ -st pile towards the $ n $ -th pile, and he wants to eat every pile of food without walking back. When Luke reaches the $ i $ -th pile, he can eat that pile if and only if $ |v - a_i| \leq x $ , where $ x $ is a fixed integer, and $ v $ is Luke's food affinity. Before Luke starts to walk, he can set $ v $ to any integer. Also, for each $ i $ ( $ 1 \leq i \leq n $ ), Luke can change his food affinity to any integer before he eats the $ i $ -th pile. Find the minimum number of changes needed to eat every pile of food. Note that the initial choice for $ v $ is not considered as a change.

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The description of test cases follows. For each test case, the first line contains two integers, $ n, x $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ , $ 1 \leq x \leq 10^9 $ ) — the number of piles, and the maximum difference between the size of a pile and Luke's food affinity, such that Luke can eat the pile. The second line contains $ n $ integers $ a_1, a_2, \ldots , a_n $ ( $ 1 \leq a_i \leq 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output an integer on a separate line, which is the minimum number of changes needed.

In the first test case, Luke can set $ v $ to $ 5 $ before he starts to walk. And he can walk straight to eat every piles of food without changing $ v $ . In the second test case, Luke can set $ v $ to $ 3 $ before he starts to walk. And he could change $ v $ to $ 10 $ before he eats the second pile. After that, he can walk straight to eat remaining food without changing $ v $ . In the fourth test case, Luke can set $ v $ to $ 3 $ before he starts to walk. And he could change $ v $ to $ 8 $ before he eats the sixth pile. After that, he can walk straight to eat remaining food without changing $ v $ . In the fifth test case, Luke can set $ v $ to $ 4 $ before he starts to walk. And he could change $ v $ to $ 6 $ before he eats the fourth pile. Then he could change $ v $ to $ 12 $ before he eats the seventh pile. After that, he can walk straight to eat remaining food without changing $ v $ .