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}.
		/*input

		*/
		import java.io.ByteArrayInputStream;
		import java.io.IOException;
		import java.io.InputStream;
		import java.io.PrintWriter;
		import java.util.*;
		import java.io.*;
		public class Main {
		InputStream is;
			PrintWriter out;
			String INPUT = ""; 
		//class Declaration
		static class pair implements Comparable<pair>{
			int x,y;
			
			pair (int i,int j)
			{ x=i; y=j;
				
			}
			public int compareTo(pair p){
				if(this.x!=p.x) { return this.x-p.x;}
				else { return this.y-p.y;}
			}
			public int hashCode() { return (x+" "+y).hashCode();}
			public String toString(){ return x+" "+y;} 
			public boolean equals(Object o){ 
				pair x = (pair) o ;
				return (x.x==this.x&&x.y==this.y);}
		}

	void solve() {
		int n=ni(),d=ni();
		ArrayList<Integer> al =new ArrayList<>();
		for(int i=0;i<n;++i){
			al.add(ni());

		}
		long ans=0;
		for(int i=0;i<n-1;++i){
			int ind=Collections.binarySearch(al,al.get(i)+d);
			if(ind<0) ind= -ind -2;
			int middlePoints = ind-i-1;
			//pn("ind "+ind);
			ans += addAll(middlePoints);
		}
		pn(ans);


	}
	long addAll(long x){
		return x*(x+1L)/2L;
	}
	ArrayList<Integer> sieve(int n){
		ArrayList<Integer> al=new ArrayList<>();
			boolean prime[] = new boolean[n+1];
			for(int i=0;i<n;i++)
				prime[i] = true;
		for(int p = 2; p*p <=n; p++)
			{
				if(prime[p])
				{
		
					for(int i = p*2; i <= n; i += p)
					prime[i] = false;
				}
			}
		for(int i = 2; i <= n; i++)
		{
			if(prime[i] == true) 
				al.add(i);
		}
			return al;
			
		}
	int gcd(int a, int b) 
	{ 
	if (b == 0) 
		return a; 
	return gcd(b, a % b);  
	} 


		void run() throws Exception
		{
				is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
				out = new PrintWriter(System.out);
				
				long s = System.currentTimeMillis();
				solve();
				out.flush();
				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
		}
			
			
			public static void main(String[] args) throws Exception { new Main().run(); }
			
		//output methods
		private void pn(Object o)
		{
			out.println(o);
		}
		private void p(Object o)
		{
			out.print(o);
		}



		//input methods
				private byte[] inbuf = new byte[1024];
			public int lenbuf = 0, ptrbuf = 0;
			

			private 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++];
			}
			
			private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
			private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
			
			private double nd() { return Double.parseDouble(ns()); }
			private char nc() { return (char)skip(); }
			
			private String ns()
			{
				int b = skip();
				StringBuilder sb = new StringBuilder();
				while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
					sb.appendCodePoint(b);
					b = readByte();
				}
				return sb.toString();
			}
			
			private char[] ns(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);
			}
				
			private char[][] nm(int n, int m)
			{
				char[][] map = new char[n][];
				for(int i = 0;i < n;i++)map[i] = ns(m);
				return map;
			}
			
			private int[] na(int n)
			{
				int[] a = new int[n];
				for(int i = 0;i < n;i++)a[i] = ni();
				return a;
			}
			
			private int ni()
			{
				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 * 10 + (b - '0');
					}else{
						return minus ? -num : num;
					}
					b = readByte();
				}
			}
			
			private long nl()
			{
				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 * 10 + (b - '0');
					}else{
						return minus ? -num : num;
					}
					b = readByte();
				}
			}
			
			private void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
		}

