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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;

// CFPS -> CodeForcesProblemSet
public final class CFPS {
	static FastReader fr = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	static final int gigamod = 1000000007;
	static int t = 1;
	public static void main(String[] args) {
		OUTER: 
		for (int tc = 0; tc < t; tc++) {
			
			int n = fr.nextInt();
			long d = fr.nextLong();
			long[] coords = fr.nextLongArray(n);
			
			// When n (>=2) points are inside the range [1, d] from some point
			// 'i', we can make nC2 combinations for this point.
			
			// SO, we iterate over each point and find out the number of
			// points that fall in its range and calculate the total number
			// of ways.
			
			if (n < 3) {
				out.println(0);
				continue OUTER;
			}
			
			long ways = 0;
			for (int i = 0; i < n; i++) {
				long finalCoord = coords[i] + d;
				int idx = bsearch(coords, finalCoord, 0, n - 1, true);
				int numPoints = idx - i;
				if (numPoints < 2) continue;
				ways += (nCr(numPoints, 2));
			}
			
			out.println(ways);
		}
		out.close();
	}
	
	static String bitSetToString(int set) {
		// We have to print all the elements that are present
		// in the set.
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < 30; i++) {
			if (((set >> i) & 1) == 1) {
				// The 'i'th bit is on meaning that the element 'i' is 
				// present in the set.
				sb.append((i + 1) + " ");
			}
		}
		sb.append("\n");
		return sb.toString();
	}
	
	static String displayBitSet(long set) {
		// We have to print all the elements that are present
		// in the set.
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < 60; i++) {
			if (((set >> i) & 1) == 1) {
				// The 'i'th bit is on meaning that the element 'i' is 
				// present in the set.
				sb.append((i + 1) + " ");
			}
		}
		sb.append("\n");
		return sb.toString();
	}
	
	static int addToBitSet(int set, int element) {
		set = (set) | (1 << (element - 1));
		return set;
	}
	
	static int removeFromBitSet(int set, int element) {
		// Checking whether the bit is present.
		if ((set & (1 << (element - 1))) == 0) return set;
		set = set ^ (1 << (element - 1));
		return set;
	}
	
	// Returns map of factor and its power in the number.
	static TreeMap<Long, Integer> primeFactorization(long num) {
		TreeMap<Long, Integer> map = new TreeMap<>();
		while (num % 2 == 0) {
			num /= 2;
			Integer pwrCnt = map.get(2L);
			map.put(2L, pwrCnt != null ? pwrCnt + 1 : 1);
		}
		
		for (long i = 3; i * i <= num; i += 2) {
			while (num % i == 0) {
				num /= i;
				Integer pwrCnt = map.get(i);
				map.put(i, pwrCnt != null ? pwrCnt + 1 : 1);
			}
		}
		
		// If the number is prime, we have to add it to the 
		// map.
		if (num != 1)
			map.put(num, 1);
		
		return map;
	}
	
	// Returns map of factor and its power in the number.
	static TreeMap<Integer, Integer> primeFactorization(int num) {
		TreeMap<Integer, Integer> map = new TreeMap<>();
		while (num % 2 == 0) {
			num /= 2;
			Integer pwrCnt = map.get(2);
			map.put(2, pwrCnt != null ? pwrCnt + 1 : 1);
		}
		
		for (int i = 3; i * i <= num; i += 2) {
			while (num % i == 0) {
				num /= i;
				Integer pwrCnt = map.get(i);
				map.put(i, pwrCnt != null ? pwrCnt + 1 : 1);
			}
		}
		
		// If the number is prime, we have to add it to the 
		// map.
		if (num != 1)
			map.put(num, 1);
		
		return map;
	}
	
	
	static void dfs(int node, boolean[] marked, ArrayList<Integer>[] adj) {
		if (marked[node]) return;

		marked[node] = true;
		for (int adjc : adj[node])
			dfs(adjc, marked, adj);
	}

	
	static class Point implements Comparable<Point> {
		long x;
		long y;
		int id;
		
		Point() {
			x = y = id = 0;
		}
		
		Point(long a, long b, int id) {
			this.x = a;
			this.y = b;
			this.id = id;
		}
		
		@Override
		public int compareTo(CFPS.Point o) {
			if (this.x > o.x)
				return 1;
			if (this.x < o.x)
				return -1;
			if (this.y > o.y)
				return 1;
			if (this.y < o.y)
				return -1;
			return 0;
		}
	}
	
	static class PointComparator implements Comparator<Point> {
		@Override
		public int compare(CFPS.Point o1, CFPS.Point o2) {
			if (o1.y > o2.y)
				return 1;
			if (o1.y < o2.y)
				return -1;
			if (o1.x > o2.x)
				return 1;
			if (o1.x < o2.x)
				return -1;
			return 0;
		}
	}
	
	// Returns the index of the first element
	// larger than or equal to val.
	static int bsearch(int[] arr, int val, int lo, int hi) {
		int idx = -1;
		while (lo <= hi) {
			int mid = lo + (hi - lo)/2;
			if (arr[mid] >= val) {
				idx = mid;
				hi = mid - 1;
			} else
				lo = mid + 1;
		}
		return idx;
	}
	
	
	static int bsearch(long[] arr, long val, int lo, int hi) {
		int idx = -1;
		while (lo <= hi) {
			int mid = lo + (hi - lo)/2;
			if (arr[mid] >= val) {
				idx = mid;
				hi = mid - 1;
			} else
				lo = mid + 1;
		}
		return idx;
	}
	
	// Returns the index of the last element 
	// smaller than or equal to val.
	static int bsearch(long[] arr, long val, int lo, int hi, boolean sMode) {
		int idx = -1;
		while (lo <= hi) {
			int mid = lo + (hi - lo)/2;
			if (arr[mid] > val) {
				hi = mid - 1;
			} else {
				idx = mid;
				lo = mid + 1;
			}
		}
		return idx;
	}
	
	static int bsearch(int[] arr, long val, int lo, int hi, boolean sMode) {
		int idx = -1;
		while (lo <= hi) {
			int mid = lo + (hi - lo)/2;
			if (arr[mid] > val) {
				hi = mid - 1;
			} else {
				idx = mid;
				lo = mid + 1;
			}
		}
		return idx;
	}
	
	static int factorial(int n) {
		if (n <= 1)
			return 1;
		return n * factorial(n - 1);
	}
	
	static long factorial(long n) {
		if (n <= 1)
			return 1;
		return n * factorial(n - 1);
	}
	
	static long factorialInDivision(long a, long b) {
		if (a == b)
			return 1;
		return a * factorialInDivision(a - 1, b);
	}
	
	static BigInteger factorialInDivision(BigInteger a, BigInteger b) {
		if (a.equals(b))
			return BigInteger.ONE;
		return a.multiply(factorialInDivision(a.subtract(BigInteger.ONE), b));
	}
	
	static long nCr(long n, long r) {
		return nPr(n, r) / factorial(r);
	}
	
	static long nPr(long n, long r) {
		return factorialInDivision(n, n - r);
	}
	
	static int log2(long n) {
		return (int)(Math.log(n) / Math.log(2));
	}
	
	// Sieve of Eratosthenes: 
	static boolean[] primeGenerator(int upto) {
		boolean[] isPrime = new boolean[upto + 1];
		Arrays.fill(isPrime, true);
		isPrime[1] = isPrime[0] = false;

		for (long i = 2; i * i < upto + 1; i++)
			if (isPrime[(int) i])
				// Mark all the multiples greater than or equal
				// to the square of i to be false.
				for (long j = i; j * i < upto + 1; j++)
					isPrime[(int) j * (int) i] = false;
		return isPrime;
	}

	static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		} else {
			return gcd(b, a % b);
		}
	}
	
	static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		} else {
			return gcd(b, a % b);
		}
	}
	
	static int gcd(int[] arr) {
		int n = arr.length;
		int gcd = arr[0];
		for (int i = 1; i < n; i++) {
			gcd = gcd(gcd, arr[i]);
		}
		return gcd;
	}
	
	static long gcd(long[] arr) {
		int n = arr.length;
		long gcd = arr[0];
		for (int i = 1; i < n; i++) {
			gcd = gcd(gcd, arr[i]);
		}
		return gcd;
	}
	
	static long lcm(int[] arr) {
		int lcm = arr[0];
		int n = arr.length;
		for (int i = 1; i < n; i++) {
			lcm = (lcm * arr[i]) / gcd(lcm, arr[i]);
		}
		return lcm;
	}
	
	static long lcm(long[] arr) {
		long lcm = arr[0];
		int n = arr.length;
		for (int i = 1; i < n; i++) {
			lcm = (lcm * arr[i]) / gcd(lcm, arr[i]);
		}
		return lcm;
	}
	
	static long lcm(int a, int b) {
		return (a * b)/gcd(a, b);
	}
	
	static long lcm(long a, long b) {
		return (a * b)/gcd(a, b);
	}
	
	static boolean less(int a, int b) {
		return a < b ? true : false;
	}
	
	static boolean isSorted(int[] a) {
		for (int i = 1; i < a.length; i++) {
			if (less(a[i], a[i - 1]))
				return false;
		}
		return true;
	}
	
	static boolean isSorted(long[] a) {
		for (int i = 1; i < a.length; i++) {
			if (a[i] < a[i - 1])
				return false;
		}
		return true;
	}

	static void swap(int a, int b) {
		int temp = a;
		a = b;
		b = temp;
	}
	
	static void swap(long a, long b) {
		long temp = a;
		a = b;
		b = temp;
	}
	
	static void swap(double a, double b) {
		double temp = a;
		a = b;
		b = temp;
	}
	
	static void swap(int[] a, int i, int j) {
		int temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	
	static void swap(long[] a, int i, int j) {
		long temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	
	static void swap(double[] a, int i, int j) {
		double temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	
	static void sort(int[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
	}
	
	static void sort(long[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
	}
	
	static void sort(double[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
	}
	
	static void reverseSort(int[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
		int n = arr.length;
		for (int i = 0; i < n/2; i++)
			swap(arr, i, n - 1 - i);
	}
	
	static void reverseSort(long[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
		int n = arr.length;
		for (int i = 0; i < n/2; i++)
			swap(arr, i, n - 1 - i);
	}
	
	static void reverseSort(double[] arr) {
		shuffleArray(arr, 0, arr.length - 1);
		Arrays.sort(arr);
		int n = arr.length;
		for (int i = 0; i < n/2; i++)
			swap(arr, i, n - 1 - i);
	}
	
	static void shuffleArray(long[] arr, int startPos, int endPos) {
		Random rnd = new Random();
		for (int i = startPos; i < endPos; ++i) {
			long tmp = arr[i];
			int randomPos = i + rnd.nextInt(endPos - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}
	
	static void shuffleArray(int[] arr, int startPos, int endPos) {
		Random rnd = new Random();
		for (int i = startPos; i < endPos; ++i) {
			int tmp = arr[i];
			int randomPos = i + rnd.nextInt(endPos - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}
	
	static void shuffleArray(double[] arr, int startPos, int endPos) {
		Random rnd = new Random();
		for (int i = startPos; i < endPos; ++i) {
			double tmp = arr[i];
			int randomPos = i + rnd.nextInt(endPos - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}

	// Time Complexity: O(sqrt(n))
	static boolean isPrime(int n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;

		if (n % 2 == 0 || n % 3 == 0)
			return false;

		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;

		return true;
	}

	static String toString(int[] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++)
			sb.append(dp[i] + "");
		return sb.toString();
	}
	
	static String toString(boolean[] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++)
			sb.append(dp[i] + " ");
		return sb.toString();
	}
	
	static String toString(long[] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++)
			sb.append(dp[i] + " ");
		return sb.toString();
	}
	
	static String toString(char[] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++)
			sb.append(dp[i] + " ");
		return sb.toString();
	}
	
	static String toString(int[][] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++) {
			for (int j = 0; j < dp[i].length; j++) {
				sb.append(dp[i][j] + " ");
			}
			sb.append('\n');
		}
		return sb.toString();
	}
	
	static String toString(long[][] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++) {
			for (int j = 0; j < dp[i].length; j++) {
				sb.append(dp[i][j] + " ");
			}
			sb.append('\n');
		}
		return sb.toString();
	}
	
	static String toString(double[][] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++) {
			for (int j = 0; j < dp[i].length; j++) {
				sb.append(dp[i][j] + " ");
			}
			sb.append('\n');
		}
		return sb.toString();
	}
	
	static String toString(char[][] dp) {
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < dp.length; i++) {
			for (int j = 0; j < dp[i].length; j++) {
				sb.append(dp[i][j] + " ");
			}
			sb.append('\n');
		}
		return sb.toString();
	}
	
	static long mod (long a, long m) {
	    return (a%m + m) % m;
	}
	
	static long mod (long num) {
		return (num % gigamod + gigamod) % gigamod;
	}
	
	// Uniform hashing into array.
	static int hash(String s, int arrayLen) {
		return (s.hashCode() & 0x7fffffff) % arrayLen;
	}
	
	static int hash(Integer s, int arrayLen) {
		return (s.hashCode() & 0x7fffffff) % arrayLen;
	}
	
	static int hash(Long s, int arrayLen) {
		return (s.hashCode() & 0x7fffffff) % arrayLen;
	}
	
	static int hash(Double s, int arrayLen) {
		return (s.hashCode() & 0x7fffffff) % arrayLen;
	}
	
	// Uses weighted quick-union with path compression.
	static class UnionFind {
	    private static int[] parent;  // parent[i] = parent of i
	    private static int[] size;    // size[i] = number of sites in tree rooted at i
	                           // Note: not necessarily correct if i is not a root node
	    private int count;     // number of components

	    public UnionFind(int n) {
	        count = n;
	        parent = new int[n];
	        size = new int[n];
	        for (int i = 0; i < n; i++) {
	            parent[i] = i;
	            size[i] = 1;
	        }
	    }

	    // Number of connected components.
	    public int count() {
	        return count;
	    }
	  
	    // Find the root of p.
	    public int find(int p) {
	        int root = p;
	        while (root != parent[root])
	            root = parent[root];
	        while (p != root) {
	            int newp = parent[p];
	            parent[p] = root;
	            p = newp;
	        }
	        return root;
	    }

	    public boolean connected(int p, int q) {
	        return find(p) == find(q);
	    }
	    
	    // Weighted union.
	    public void union(int p, int q) {
	        int rootP = find(p);
	        int rootQ = find(q);
	        
	        if (rootP == rootQ) return;

	        // make smaller root point to larger one
	        if (size[rootP] < size[rootQ]) {
	            parent[rootP] = rootQ;
	            size[rootQ] += size[rootP];
	        }
	        else {
	            parent[rootQ] = rootP;
	            size[rootP] += size[rootQ];
	        }
	        count--;
	    }
	}
	
	static class UGraph {
		// Adjacency list.
		private HashSet<Integer>[] adj;
		private static final String NEWLINE = "\n";
		private int E;
		
		public UGraph(int V) {
			adj = (HashSet<Integer>[]) new HashSet[V];
			E = 0;
			for (int i = 0; i < V; i++)
				adj[i] = new HashSet<Integer>();
		}
		
		public void addEdge(int from, int to) {
			if (adj[from].contains(to)) return;
			E++;
			adj[from].add(to);
			adj[to].add(from);
		}
		
		public Iterable<Integer> adj(int from) {
			return adj[from];
		}
		
		public int V() {
			return adj.length;
		}
		
		public int E() {
			return E;
		}
		
		public String toString() {
			StringBuilder s = new StringBuilder();
			s.append(V() + " vertices, " + E() + " edges " + NEWLINE);
			for (int v = 0; v < V(); v++) {
				s.append(v + ": ");
				for (int w : adj[v]) {
					s.append(w + " ");
				}
				s.append(NEWLINE);
			}
			return s.toString();
		}
		
		public static void dfsMark(int source, boolean[] marked, UGraph g) {
			if (marked[source]) return;
			
			marked[source] = true;
			Iterable<Integer> adj = g.adj(source);
			for (int adjc : adj)
				dfsMark(adjc, marked, g);
		}
		
		public static void bfsOrder(int source, UGraph g) {
		}
		
		private static void dfsMark(int source, int[] colorIds, int color, UGraph g) {
			if (colorIds[source] != -1) return;
			
			colorIds[source] = color;
			Iterable<Integer> adj = g.adj(source);
			for (int adjc : adj)
				dfsMark(adjc, colorIds, color, g);
		}
		
		public static int[] connectedComponents(UGraph g) {
			int n = g.V();
			int[] componentId = new int[n];
			Arrays.fill(componentId, -1);
			int colorCtr = 0;
			for (int i = 0; i < n; i++) {
				if (componentId[i] != -1) continue;
				dfsMark(i, componentId, colorCtr, g);
				colorCtr++;
			}
			
			return componentId;
		}
	}
	
	static class FastReader {
		private BufferedReader bfr;
		private StringTokenizer st;

		public FastReader() {
			bfr = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			if (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(bfr.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		char nextChar() {
			return next().toCharArray()[0];
		}

		String nextString() {
			return next();
		}

		int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				arr[i] = nextInt();
			return arr;
		}
		
		int[] nextOneIntArray(int n) {
			int[] arr = new int[n + 1];
			for (int i = 1; i < n; i++)
				arr[i] = nextInt();
			return arr;
		}

		double[] nextDoubleArray(int n) {
			double[] arr = new double[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextDouble();
			return arr;
		}

		long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++)
				arr[i] = nextLong();
			return arr;
		}

		public char[] nextCharArray(int n) {
			char[] chars = new char[n];
			for (int i = 0; i < n; i++)
				chars[i] = fr.nextChar();
			return chars;
		}
	}
}

// NOTES: 
// ASCII VALUE OF 'A': 65
// ASCII VALUE OF 'a': 97
// Range of long: 9 * 10^18
// ASCII VALUE OF '0': 48