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 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 = a₁a₂... a_la_ra_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 ≤ 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, ..., a_n (1 ≤ a_i ≤ 10⁹) — 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.

Little Elephant and Inversions

Examples