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.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        long d = in.nextInt();
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) arr[i] = in.nextLong();
        long res = 0;
        for (int i = 0; i < n; i++) {
            long D = upperBound(arr, n, i, (arr[i] + d));
            res += nCr(D - i);
        }
        pw.println(res);
        pw.close();
    }

    static long nCr(long n) {
        return n * 1L * (n - 1) / 2;
    }

    static int upperBound(long[] arr, int n, int left, long val) {
        int res = 0;
        int right = n - 1;
        // debug(left, val);
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (arr[mid] > val) {
                right = mid - 1;
            } else {
                left = mid + 1;
                res = mid;
            }
        }
       // debug(res);
        return res;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }


        public String nextLine() {
            int c = skip();
            StringBuilder sb = new StringBuilder();
            while (!isEndOfLine(c)) {
                sb.appendCodePoint(c);
                c = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

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

        public char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        public char readChar() {
            return (char) skip();
        }
    }
}
	  		 	 	    		 		   	 			 	