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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import sys
sys.setrecursionlimit(10**6)
input = sys.stdin.readline

class BIT:
    def __init__(self,n,default = 0):
        self.s = [default]*(n+1)
    
    def add(self,val,idx):
        while idx < n+1:
            self.s[idx] = self.s[idx] + val
            idx += idx&(-idx)
        return
    
    def get(self,idx):
        res = 0
        while idx > 0:
            res = res + self.s[idx]
            idx -= idx&(-idx)
        return res


n,k = map(int,input().split())
ans = 0
s = [0]*(n+1)
array = {0}
for i in range(n):
    s[i+1] = s[i] + int(input()) - k
    array.add(s[i+1])
array = sorted(array)
d = {x:i for i,x in enumerate(array)}
bit = BIT(len(array))
for t in s:
    ans += bit.get(d[t]+1)
    bit.add(1,d[t]+1)
print(ans)