Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Little Elephant and Inversions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Little Elephant has array *a*, consisting of *n* positive integers, indexed from 1 to *n*. Let's denote the number with index *i* as *a*_{i}.

The Little Elephant wants to count, how many pairs of integers *l* and *r* are there, such that 1 ≤ *l* < *r* ≤ *n* and sequence *b* = *a*_{1}*a*_{2}... *a*_{l}*a*_{r}*a*_{r + 1}... *a*_{n} has no more than *k* inversions.

An inversion in sequence *b* is a pair of elements of the sequence *b*, that change their relative order after a stable sorting of the sequence. In other words, an inversion is a pair of integers *i* and *j*, such that 1 ≤ *i* < *j* ≤ |*b*| and *b*_{i} > *b*_{j}, where |*b*| is the length of sequence *b*, and *b*_{j} is its *j*-th element.

Help the Little Elephant and count the number of the described pairs.

Input

The first line contains two integers *n* and *k* (2 ≤ *n* ≤ 10^{5}, 0 ≤ *k* ≤ 10^{18}) — the size of array *a* and the maximum allowed number of inversions respectively. The next line contains *n* positive integers, separated by single spaces, *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}) — elements of array *a*.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Output

In a single line print a single number — the answer to the problem.

Examples

Input

3 1

1 3 2

Output

3

Input

5 2

1 3 2 1 7

Output

6

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/20/2018 10:16:23 (d2).

Desktop version, switch to mobile version.

User lists

Name |
---|