B. Luke is a Foodie
brute force; greedy; implementation
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 \(v\).