A8840. Points on Line

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.

The first line contains two integers: $n$ and $d$ ( $1<=n<=10^{5}; 1<=d<=10^{9}$ ). The next line contains $n$ integers $x_{1},x_{2},...,x_{n}$ , their absolute value doesn't exceed $10^{9}$ — the $x$ -coordinates of the points that Petya has got.

It is guaranteed that the coordinates of the points in the input strictly increase.

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.

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}.