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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <cstdint>
#include <cinttypes>
#include <iostream>
#include <vector>
#include <utility>
#include <cmath>
#include <algorithm>
#include <numeric>
#include <string>
using u8t = std::uint64_t;
using i8t = std::int64_t;
#define F(I,N) for(i8t I=0,_N=N;I<_N;I++)
#define R(V) i8t V;std::cin>>V;
#define RV(V,N) std::vector<i8t> V;F(i,N){R(x)V.push_back(x);}
#define RL1(line) std::getline(std::cin,line);
#define RL(line) std::string line;RL0(line)
#define P(X) std::cout<<(X)<<std::endl;
int main() {
  R(N)R(K)RV(a,N);
  std::vector<i8t> s;
  i8t sum = 0;
  s.push_back(0);
  F(i,N){
    auto d = a[i] - K;
    sum+=d;
    s.push_back(sum);
  }

  struct tt{i8t index,value;};
  std::vector<tt> ss;
  F(i,N+1){
    tt v;
    v.index=i;
    v.value=s[i];
    ss.push_back(v);
  }
  std::sort(ss.begin(),ss.end(),[](auto const& lhs,auto const& rhs){return lhs.value!=rhs.value?lhs.value<rhs.value:lhs.index<rhs.index;});

  i8t count = 0;

  //N <= 2e5 = 200000 <= 1024 * 200 <= 2^18
  std::vector<std::vector<i8t> > tbl(18);
  for(int i = 0;i<18;i++){tbl[i].resize(std::pow(2, 18-i),0);}

  F(i,N+1){s[ss[i].index]=i;}
  F(i,N+1){
    i8t ind=s[i];
    i8t c1=0;
    for(i8t j=0;j<18;j++,ind>>=1){
      if(ind&1)c1+=tbl[j][ind&~1];
      tbl[j][ind]++;
    }
    count+=c1;
  }
  P(count);
  return 0;
}