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 \le l \lt r \le 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 \le i \lt j \le |b| and bi \gt 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.

The first line contains two integers n and k (2 \le n \le 105,0 \le k \le 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 \le ai \le 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.

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