Problem3724--Little Elephant and Inversions

3724: Little Elephant and Inversions

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The Little Elephant has array a, consisting of n positive integers, indexed from 1 to n. Let's denote the number with index i as ai.

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=a1a2... alarar+1... an 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 bi>bj, where |b| is the length of sequence b, and bj 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≤105,0≤k≤1018) − the size of array a and the maximum allowed number of inversions respectively. The next line contains n positive integers, separated by single spaces, a1,a2,...,an (1≤ai≤109) − elements of array a.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. 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

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