Codeforces 251A Points on line (binary or monotone queue)

Description

Little Petya likes points a lot. Recently his mom had presented him N points lying on the line OX. Now Petya are wondering in what many ways he can choose three distinct points so that the distance between the 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 the integers: n and D (1≤ n ≤10^{5; 1≤ D ≤10 9). The next line contains n integers x_{1, x2, ..., x c17>n, their absolute value doesn ' t exceed ten9-the x-coordinates of the points that Petya has got.}}

It is guaranteed, 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 both farthest points doesn ' t exce Ed D.

%lld specifier to read or write 64-bit integers inс++. It is preferred to use the CIN, cout streams or the %i64dspecifier.

Sample Input

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

Hint

In the first sample any group of three points meets our conditions.

In the seconds sample is 2 groups of three points meet our conditions: { -3,-2,-1} and {-2,-1, 0}.

In the third sample is only one group does: {1, ten, +}.

Test instructions: Given an ascending sequence, find out 3 numbers from this sequence, and the difference between the maximum and the minimum is less than or equal to the number of K.

Idea: A bit of a recursive feeling, each added in a number, only consider the contribution of this number, for example, add in the 5th number, assuming that the preceding four numbers meet the requirements, then 5 of the contribution is to remove two from the preceding 4 number of total, so is C 4 2, this is a combination of numbers. So consider each number and add up the combined number of each number.

Code one (monotone queue);

#include <cstdio>#include<iostream>#include<cstring>#include<cmath>#include<cstdlib>#include<algorithm>using namespaceStd;typedefLong Longll;Const intMAXN =100010;intA[MAXN];intQ[MAXN];intMain () {intN, D; scanf ("%d%d", &n, &d); ll ans=0; intFront =1, tail =0;  for(inti =0; I < n; i++) {scanf ("%d", &A[i]); q[++tail] =A[i];  while(Tail >= front && Q[front] < a[i]-D) front++; intj = Tail-Front; Ans+ = (LL) J * (J-1) /2;//C N 2} printf ("%i64d\n", ans); return 0;}

Code two (two points):

#include <cstdio>#include<iostream>#include<cstring>#include<cmath>#include<cstdlib>#include<algorithm>using namespaceStd;typedefLong Longll;Const intMAXN =100010;intA[MAXN];intMain () {intN, D; scanf ("%d%d", &n, &d); ll ans=0;  for(inti =0; I < n; i++) scanf ("%d", &A[i]);  for(inti =1; I < n; i++)    {        intj = i-(Lower_bound (A, A + I, a[i]-D)-a); Ans+ = (LL) J * (J-1) /2; } printf ("%i64d\n", ans); return 0;}

Codeforces 251A Points on line (binary or monotone queue)