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
    def initialize(n)
        @n = n+1
        @dat = Array.new(@n+1, 0)
    end

    def sum(i)
        s = 0
        while i >= 0 do
            s += @dat[i]
            i = (i & (i + 1)) - 1
        end
        s
    end

    def add(i, x)
        while i <= @n do
            @dat[i] += x
            i |= i + 1
        end
    end
end

N, K = gets.split.map(&:to_i)
as = N.times.map{gets.to_i - K}
partsum = [0]
(0...N).each do |i|
    partsum[i+1] = partsum[i] + as[i]
end

sum2order = {}
partsum.sort.each_with_index do |sum, order|
    sum2order[sum] = order
end

compress = partsum.map{|sum|sum2order[sum]}

bit = BIT.new(N)
ans = 0
(N+1).times do |j|
    ans += bit.sum(compress[j])
    bit.add(compress[j], 1)
end

puts ans