Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d.

Note that the order of the points inside the group of three chosen points doesn't matter.

Input

The first line contains two integers: n and d (1 ≤ n ≤ 105; 1 ≤ d ≤ 109). The next line contains n integers x1, x2, ..., xn, their absolute value doesn't exceed 109 — the x-coordinates of the points that Petya has got.

It is guaranteed that the coordinates of the points in the input strictly increase.

Output

Print a single integer — the number of groups of three points, where the distance between two farthest points doesn't exceed d.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

4 3
1 2 3 4


Output

4


Input

4 2
-3 -2 -1 0


Output

2


Input

5 19
1 10 20 30 50


Output

1

Note

In the first sample any group of three points meets our conditions.

In the seconds sample only 2 groups of three points meet our conditions: {-3, -2, -1} and {-2, -1, 0}.

In the third sample only one group does: {1, 10, 20}.
import java.util.*;
import java.io.*;
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////////                                                                                            /////////
////////                                                                                            /////////
////////   MMMM          MMMM    AAAAAAAAAAAAAAAAA  RRRRRRRRRR       EEEEEEEEEEEEE  DDDDDDDDD       /////////
////////   MMMMMM      MMMMMM    AAAAAAAAAAAAAAAAA  RRRR     RRR     EEEEEEEEEEEEE  DDD     DDD     /////////
////////   MMMM MMM  MMM MMMM    AAAA         AAAA  RRRR      RRR    EEEEE          DDD      DDD    /////////
////////   MMMM  MMMMM   MMMM    AAAA         AAAA  RRRR       RRR   EEEEE          DDD       DDD   /////////
////////   MMMM          MMMM    AAAA         AAAA  RRRR      RRR    EEEEE          DDD        DDD  /////////
////////   MMMM          MMMM    AAAA         AAAA  RRRR     RRR     EEEEEEEEEEE    DDD         DDD /////////
////////   MMMM          MMMM    AAAAAAAAAAAAAAAAA  RRRRRRRRRR       EEEEEEEEEEE    DDD         DDD /////////
////////   MMMM          MMMM    AAAAAAAAAAAAAAAAA  RRRR    RRR      EEEEE          DDD        DDD  /////////
////////   MMMM          MMMM    AAAA         AAAA  RRRR     RRR     EEEEE          DDD      DDD    /////////
////////   MMMM          MMMM    AAAA         AAAA  RRRR      RRR    EEEEEEEEEEEEE  DDD    DDD      /////////
////////   MMMM          MMMM    AAAA         AAAA  RRRR       RRR   EEEEEEEEEEEEE  DDDDDDDDD       /////////
////////                                                                                            /////////
////////                                                                                            /////////
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/////////////////////////////////////////////////////////////////////////////////////////////////////////////

public class PointsOnLine {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt(); int d = sc.nextInt();
        if(n==1 || n==2){out.println(0); out.flush(); return;}
        long[] arr = new long[n];
        for(int i = 0; i<n; i++){
            arr[i] = sc.nextLong();
        }
        long counter = 0;
        int start = 0; int end = 1;
        while(start<n){
            while(end<n && arr[end]-arr[start]<=d){
                end++;
            }
            long points = end-start-1;
            counter = counter + (points*(points-1)/2);
            start++;
        }
        out.println(counter);
        out.flush();

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
    }
}