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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

n,k=map(int,input().split())
A=[]
for i in range(n):
  A.append(int(input())-k)
AA,BB=[0]*(n+1),[0]*(n+1)
AA[-2]=A[-1]
BB[-2]=A[-1]
for i in reversed(range(n-1)):
  AA[i]=AA[i+1]+A[i]
  BB[i]=BB[i+1]+A[i]
BB.sort()
cur=1
D=dict()
D[BB[0]]=cur
for i in range(1,n+1):
  if BB[i]==BB[i-1]:
    continue
  else:
    cur+=1
    D[BB[i]]=cur
AAA=[0]*(n+1)
for i in range(n+1):
  AAA[i]=D[AA[i]]

import math
n_max=2*10**5
nn=int(math.log2(n_max))+1
BIT=[0]*(2**nn)
BIT.insert(0,0)
def bitsum(BIT,i):
  s=0
  while i>0:
    s+=BIT[i]
    i-=i&(-i)
  return s
def bitadd(BIT,i,x):
  while i<=2**nn:
    BIT[i]+=x
    i+=i&(-i)
  return BIT

ans=0
for i in range(n+1):
  ans+=i-bitsum(BIT,AAA[i]-1)
  bitadd(BIT,AAA[i],1)
print(ans)