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.*;
public final class code
{
	static int n,d,x[];
	static int bin_search(int i,int low,int high)
	{
		int ans=-1;
		while(low<=high)
		{
			int mid=(low+high)/2;
			if(x[mid]-x[i]<=d)
			{
				ans=mid;
				low=mid+1;
			}
			else
				high=mid-1;
		}
		return ans;
	}
	static void solve()throws IOException
	{
		n=nextInt();
		d=nextInt();
		x=new int[n+1];
		for(int i=1;i<=n;i++)
			x[i]=nextInt();
		long ans=0;
		for(int i=1;i<=n;i++)
		{
			int j=bin_search(i,i+1,n);
			if(j!=-1)
			ans+=(((long)(j-i))*(j-i-1))/2;
		}
		out.println(ans);
	}






	
	///////////////////////////////////////////////////////////
	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter out;
	static String nextToken()throws IOException
	{
		while(st==null || !st.hasMoreTokens())
			st=new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	static String nextLine()throws IOException
	{
		return br.readLine();
	}
	static int nextInt()throws IOException
	{
		return Integer.parseInt(nextToken());
	}
	static long nextLong()throws IOException
	{
		return Long.parseLong(nextToken());
	}
	static double nextDouble()throws IOException
	{
		return Double.parseDouble(nextToken());
	}
	public static void main(String args[])throws IOException
	{
		br=new BufferedReader(new InputStreamReader(System.in));
		out=new PrintWriter(new BufferedOutputStream(System.out));
		solve();
		out.close();
	}
}