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



Sample input:
3 6
7
5
7


Sample output:
5

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict, deque, Counter, OrderedDict
from bisect import bisect_left, bisect_right
from functools import reduce, lru_cache
from heapq import heappush, heappop, heapify

import itertools
import math, fractions
import sys, copy

def L(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline().rstrip())
def SL(): return list(sys.stdin.readline().rstrip())
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI1(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LS(): return [list(x) for x in sys.stdin.readline().split()]
def R(n): return [sys.stdin.readline().strip() for _ in range(n)]
def LR(n): return [L() for _ in range(n)]
def IR(n): return [I() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def LIR1(n): return [LI1() for _ in range(n)]
def SLR(n): return [SL() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]

def perm(n, r): return math.factorial(n) // math.factorial(r)
def comb(n, r): return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))

def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if args else [default for _ in range(n)]

dire = [[1, 0], [0, 1], [-1, 0], [0, -1]]
dire8 = [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]
alphabets = "abcdefghijklmnopqrstuvwxyz"
ALPHABETS = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
MOD = 1000000007
INF = float("inf")

sys.setrecursionlimit(1000000)

class BIT:
    def __init__(self, li):
        self.n, self.data = len(li) + 1, [0] + li
        for i in range(1, self.n):
            if i + (i & -i) < self.n: self.data[i + (i & -i)] += self.data[i]

    def add(self, i, a):
        i += 1
        while i < self.n:
            self.data[i] += a
            i += i & -i

    # sum of [0, i)
    def acc(self, i):
        res = 0
        while i > 0:
            res += self.data[i]
            i -= i & -i
        return res

    # sum of [l, r)
    def get(self, l, r = None):
        if r is None: r = l+1
        return self.acc(r) - self.acc(l)



def main():
    N, K = LI()
    A = IR(N)
    B = [ai - K for ai in A]
    cum = list(itertools.accumulate(B))
    mapping = {}
    count = 0
    for ci in sorted(cum):
        if not ci in mapping:
            mapping[ci] = count
            count += 1
    mappedcum = [mapping[ci] for ci in cum]

    bit = BIT([0]*N)

    ans = 0
    for i, ci in enumerate(mappedcum):
        ans += bit.acc(ci+1)
        if cum[i] >= 0: ans += 1
        bit.add(ci, 1)

    print(ans)


if __name__ == '__main__':
    main()