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: Accepted)

n,k = map(int,input().split())
a = [0] + [int(input())-k for _ in range(n)]

for i in range(n):
  a[i+1] += a[i]
  
def comp(lis):
  dic = {x:i+1 for i,x in enumerate(sorted(list(set(lis))))}
  return list(map(lambda x:dic[x],lis))

a = comp(a)
 
class BIT:
    def __init__(self,n):
        self.n = n
        self.size = 1<<((n-1).bit_length())
        self.bit = [0]*(self.size+1)

    def bitsum(self,idx):
        tmp = 0
        while idx:
            tmp += self.bit[idx]
            idx -= idx & -idx
        return tmp

    def bitadd(self,idx,x):
        while idx <= self.n:
            self.bit[idx] += x
            idx += idx & -idx
        return

bit = BIT(max(a))
ans = 0
for x in a:
    ans += bit.bitsum(x)
    bit.bitadd(x,1)
print(ans)