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}.
#Tardes de coding. Problem C: Points On Line
def main():
	(n,d) = (int(inp) for inp in input().split())
	coords = [int(coord) for coord in input().split()]
	groups_points = 0
	for i in range(0, n-2):
		find = coords[i] + d
		index = binary_search(find,coords,i,n-1)
		#number of numbers that there are between index and i
		aux = index - i
		groups_points += aux*(aux-1)//2
	print(groups_points)
	return groups_points

#we return the index of num or of the first num that is less than num
def binary_search(num, coords,start,end):
	if end <= start :
		if num == coords[start]:
			return start
		else: 
			index = start
			while coords[index] > num:
				index-=1
			return index
	else:
		middle = (end+start)//2
		if coords[middle] == num:
			return middle
		elif coords[middle] > num:
			return binary_search(num, coords, start, middle-1)
		else:
			return binary_search(num,coords,middle+1, end)

if __name__ == "__main__":
	main()