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 <iostream>
#include <vector>
#include <algorithm>
#include <string>

#define REP(i, a, b) for (int i = int(a); i < int(b); i++)
#define dump(val) cerr << __LINE__ << ":\t" << #val << " = " << (val) << endl

using namespace std;

typedef long long int lli;

template<typename T>
vector<T> make_v(size_t a, T b) {
    return vector<T>(a, b);
}

template<typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

template<class T>
class BIT {
public:
    vector<T> v;
    BIT(int n) {
        v.resize(n + 1, 0);
    }
    void add(int pos, T x) {
        pos++;
        for (; pos < static_cast<int>(v.size()); pos += (pos & (-pos))) {
            v[pos] += x;
        }
    }
    T get(int pos) {
        pos++;
        T ans = 0;
        for (; pos > 0; pos -= (pos & (-pos))) {
            ans += v[pos];
        }
        return ans;
    }
};

int main() {
    int N, K;
    cin >> N >> K;
    vector<lli> A(N + 1, 0);
    REP(i, 0, N) {
        cin >> A[i + 1];
        A[i + 1] -= K;
    }
    REP(i, 0, N) {
        A[i + 1] += A[i];
    }
    vector<lli> B(begin(A), end(A));
    sort(begin(B), end(B));
    B.erase(unique(begin(B), end(B)), end(B));
    REP(i, 0, N + 1) {
        A[i] = lower_bound(begin(B), end(B), A[i]) - begin(B);
    }
    lli ans = 0;
    BIT<lli> bt(N + 1);
    REP(i, 0, N + 1) {
        ans += bt.get(A[i]);
        bt.add(A[i], 1);
    }
    cout << ans << endl;
    return 0;
}