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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;

/**
 * 111118315581
 *
 * -3 3 2 3 2 3 2 3 -3 3 -3 3 -3 3 2 3
 *
 * @author pttrung
 */
public class C {

    //   public static long x, y, gcd;
    //   public static int Mod = 1000000007;
    public static int length, node;

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        //   System.out.println(Integer.MAX_VALUE);
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        int n = in.nextInt();
        int k = in.nextInt();
        int[] data = new int[n];
        TreeSet<Node> set = new TreeSet();
        for (int i = 0; i < n; i++) {
            data[i] = in.nextInt();
            set.add(new Node(data[i], i));
        }
        if (n >= 3) {
            long result = 0;
            long[] pre = new long[n + 1];
            pre[2] = 1;
            for (int i = 3; i < pre.length; i++) {
                pre[i] = pre[i - 1] * (i) / (i - 2);
            }
            for (int i = 2; i < n; i++) {
                int val = data[i] - k;
                Node node = set.ceiling(new Node(val, 0));
                if (node != null) {
                    int total = i - node.index;
                    result += pre[total];
                }
            }
            out.println(result);
        } else {
            out.println(0);
        }

        out.close();
    }

    public static class Node implements Comparable<Node> {

        int val, index;

        public Node(int val, int index) {
            this.val = val;
            this.index = index;
        }

        @Override
        public int compareTo(Node o) {
            return val - o.val;
        }
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

//    public static void extendEuclid(long a, long b) {
//        if (b == 0) {
//            x = 1;
//            y = 0;
//            gcd = a;
//            return;
//        }
//        extendEuclid(b, a % b);
//        long x1 = y;
//        long y1 = x - (a / b) * y;
//        x = x1;
//        y = y1;
//
//    }
    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
