Problem:
Score : 600 points

Problem Statement

You are given an integer sequence of length N, a = {a_1, a_2, …, a_N}, and an integer K.

a has N(N+1)/2 non-empty contiguous subsequences, {a_l, a_{l+1}, …, a_r} (1 ≤ l ≤ r ≤ N). Among them, how many have an arithmetic mean that is greater than or equal to K?

Constraints

All input values are integers.

1 ≤ N ≤ 2 \times 10^5

1 ≤ K ≤ 10^9

1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N K
a_1
a_2
:
a_N

Output

Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.

Sample Input 1

3 6
7
5
7

Sample Output 1

5

All the non-empty contiguous subsequences of a are listed below:

{a_1} = {7}

{a_1, a_2} = {7, 5}

{a_1, a_2, a_3} = {7, 5, 7}

{a_2} = {5}

{a_2, a_3} = {5, 7}

{a_3} = {7}

Their means are 7, 6, 19/3, 5, 6 and 7, respectively, and five among them are 6 or greater. Note that {a_1} and {a_3} are indistinguishable by the values of their elements, but we count them individually.

Sample Input 2

1 2
1

Sample Output 2

0

Sample Input 3

7 26
10
20
30
40
30
20
10

Sample Output 3

13

Solution in Ruby (2.3.3) (judge verdict: Accepted)

class BIT
  attr_reader :bit
  def initialize(n)
    @n = n
    @bit = Array.new(@n + 1, 0)
  end
  def sum(i)
    s = 0
    while i > 0
      s +=  @bit[i]
      i -= i & -i
    end
    return s
  end
  def add(i, x)
    i += 1
    while i <= @n
      @bit[i] += x
      i += i & -i
    end
  end
end

n, k = gets.chomp.split(" ").map(&:to_i)
a = [0]
a += readlines.map{|x| x.chomp.to_i - k}

b = [0]
n.times do |i|
  b << b[i] + a[i+1]
end

b_s = b.sort
c = b.map{|e| b_s.bsearch_index{|x| x >= e}}

bit = BIT.new(n+1)

ans = 0
c.each do |i|
  ans += bit.sum(i+1)
  bit.add(i, 1)
end
puts ans