B. Luke is a Foodietime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLuke 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.InputThe 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.OutputFor each test case, output an integer on a separate line, which is the minimum number of changes needed.ExampleInput
75 33 8 5 6 75 33 10 9 8 712 825 3 3 17 8 6 1 16 15 25 17 2310 21 2 3 4 5 6 7 8 9 108 22 4 6 8 6 4 12 148 22 7 8 9 6 13 21 2815 511 4 13 23 7 10 5 21 20 11 17 5 29 16 11Output
0
1
2
1
2
4
6
NoteIn 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.
75 33 8 5 6 75 33 10 9 8 712 825 3 3 17 8 6 1 16 15 25 17 2310 21 2 3 4 5 6 7 8 9 108 22 4 6 8 6 4 12 148 22 7 8 9 6 13 21 2815 511 4 13 23 7 10 5 21 20 11 17 5 29 16 11
0 1 2 1 2 4 6 
['brute force', 'greedy', 'implementation', '*1000']