F. Good Pairs time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n integers and an integer k.A pair (l,r) is good if there exists a sequence of indices i_1, i_2, \dots, i_m such that   i_1=l and i_m=r;  i_j < i_{j+1} for all 1 \leq j < m; and  |a_{i_j}-a_{i_{j+1}}| \leq k for all 1 \leq j < m. Find the number of pairs (l,r) (1 \leq l \leq r \leq n) that are good.InputEach test contains multiple test cases. The first line contains a single integer t (1 \leq t \leq 10^5) — the number of test cases. The description of the test cases follows.The first line of each test case contains two space-separated integers n and k (1 \leq n \leq 5 \cdot 10^5; 0 \leq k \leq 10^5) — the length of the array a and the integer k.The second line of each test case contains n space-separated integers a_1,a_2,\ldots,a_n (1 \leq a_i \leq 10^5) — representing the array a.It is guaranteed that the sum of n over all test cases does not exceed 5 \cdot 10^5.OutputFor each test case, print the number of good pairs.ExampleInput
43 01 1 14 24 8 6 86 47 2 5 8 3 820 23110 57 98 14 20 1 60 82 108 37 82 73 8 46 38 35 106 115 58 112Output
6
9
18
92
NoteIn the first test case, good pairs are (1,1), (1,2), (1,3), (2,2), (2,3), and (3,3).In the second test case, good pairs are (1,1), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4) and (4,4). Pair (1,4) is good because there exists a sequence of indices 1, 3, 4 which satisfy the given conditions.
43 01 1 14 24 8 6 86 47 2 5 8 3 820 23110 57 98 14 20 1 60 82 108 37 82 73 8 46 38 35 106 115 58 112
6 9 18 92 
['binary search', 'data structures', 'dp', '*2600']