AT_abc444_e [ABC444E] Sparse Range

You are given an integer sequence of length $ N $ , $ (A_1,\dots,A_N) $ , and a positive integer $ D $ . Find the number of pairs of integers $ (L,R) $ that satisfy both of the following conditions: - $ 1 \leq L \leq R \leq N $ - Any two elements of $ (A_L,A_{L+1},\dots,A_R) $ have a difference of at least $ D $ . - That is, $ |A_i-A_j|\geq D $ for all pairs of integers $ (i,j) $ satisfying $ L \leq i < j \leq R $ .

The input is given from Standard Input in the following format: > $ N $ $ D $ $ A_1 $ $ \dots $ $ A_N $

Output the answer.

### Sample Explanation 1 The eight pairs $ (1,1),(2,2),(3,3),(4,4),(5,5),(2,3),(3,4),(4,5) $ satisfy the conditions. ### Constraints - $ 2\leq N \leq 4\times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - $ 1 \leq D \leq 10^9 $