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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using Int = long long;
int N, K;
vector<Int> A, S;
int recur(int i, int j)
{
    if (j - i <= 0) return 0;
    if (j - i == 1) return A[i] >= K;
    vector<Int> B, C;
    int mid = (i + j) / 2;
    for (int t = i; t < mid; t++) B.push_back(S[mid] - S[t] - K*(mid-t));
    for (int t = mid+1; t <= j; t++) C.push_back(S[t] - S[mid] - K*(t-mid));
    sort(begin(B), end(B));
    sort(rbegin(C), rend(C));
    int u = 0;
    int ans = 0;
    for (int t = 0; t < B.size(); t++) {
        while (u < C.size() && B[t] + C[u] >= 0) u++;
        ans += u;
    }
    return ans + recur(i, mid) + recur(mid, j);
}
int main()
{
    cin >> N >> K;
    A.resize(N);
    S.resize(N+1);
    for (int i = 0; i < N; i++) {
        cin >> A[i];
        S[i+1] = S[i] + A[i];
    }
    cout << recur(0, A.size()) << '\n';
    return 0;
}