Problem Description

There are $ N $ cities numbered $ 1, 2, ..., N $. These cities are arranged in a straight line in this order. For each $ i $ ($1 \leq i \leq N$), the coordinate of city $ i $ is $ X_i $.

Takahashi chooses the means of transportation between city $ i $ and city $ j $ as follows:

• If the distance between city $ i $ and city $ j $, $ |X_i - X_j| $, is $ D $ or less, he walks.
• Otherwise, he takes the train.

Find the number of triples of city indices $ (i, j, k) $ that satisfy the following conditions:

• $ i < j < k $
• Takahashi walks between city $ i $ and city $ j $, and between city $ j $ and city $ k $.
• Takahashi takes the train between city $ i $ and city $ k $.

Input Format

The input is given from the standard input in the following format:

$ N $ $ D $ $ X_1 $ $ X_2 $ $ ... $ $ X_N $

Output Format

Output the answer.

Sample Input and Output

Sample Input #1

5 7
11 13 17 19 23

Sample Output #1

5

Sample Input #2

4 10
0 3 6 10

Sample Output #2

0

Sample Input #3

6 36
0 5 32 48 69 71

Sample Output #3

4

Sample Input #4

6 405885562
133510576 158828561 245133494 461153833 840383806 867039395

Sample Output #4

6

Notes/Hints

Constraints

• $3 \leq N \leq 10^5$
• $0 \leq X_i \leq 10^9$ ($1 \leq i \leq N$)
• $ X_i < X_{i + 1} $ ($1 \leq i < N$)
• $0 \leq D \leq 10^9$

Sample Explanation 1

The triples $ (i, j, k) $ that satisfy the conditions are $ (1, 2, 4) $, $ (1, 3, 4) $, $ (1, 3, 5) $, $ (2, 3, 5) $, and $ (2, 4, 5) $, totaling 5.

见题面 Input 部分

见题面 Output 部分