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 (Clang 3.8.0) (judge verdict: Accepted)

#include <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <bitset>
#include <algorithm>
#include <functional>
#include <utility>
#include <iomanip>

#define int long long int
#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

typedef pair<int, int> P;

const int INF = 1e15;
const int MOD = 1e9+7;


template <typename T>
class segment_tree{
    private:
        static int calc_size(int n){
            int m = 1;
            while(m < n){
                m *= 2;
            }
            return m;
        }

        T query(int s, int t, int i, int l, int r) const {
            if(r <= s || t <= l){
                return init;
            }

            if(s <= l && r <= t){
                return node[i];
            }

            int m = l + (r - l) / 2;
            T vl = query(s, t, i * 2 + 1, l, m);
            T vr = query(s, t, i * 2 + 2, m, r);
            return f(vl, vr);
        }

    public:
        int n;
        vector<T> node;
        T init;
        function<T(T, T)> f;

        segment_tree(int n, T init, function<T(T, T)> f)
            : n(calc_size(n)), node(calc_size(n) * 2, init), init(init), f(f){}

        void update(int i, const T& x){
            i += (n - 1);
            node[i] = x;
            while(i > 0){
                i = (i - 1) / 2;
                node[i] = f(node[2*i+1], node[2*i+2]);
            }
        }

        //[s, t)
        T query(int s, int t) const {
            return query(s, t, 0, 0, n);
        }
};

signed main(){
    int n, k;
    cin >> n >> k;

    vector<int> a(n);
    rep(i, n){
        cin >> a[i];
        a[i] -= k;
    }

    vector<int> s(n+1);
    rep(i, n){
        s[i+1] = s[i] + a[i];
    }

    vector<int> t = s;
    sort(t.begin(), t.end());
    map<int, int> encode;
    vector<int> decode;
    int m = 0;
    rep(i, n+1){
        if(encode.find(t[i]) == encode.end()){
            encode.emplace(t[i], m++);
            decode.push_back(t[i]);
        }
    }

    int ans = 0;
    //Range Sum Query
    segment_tree<int> st(m+1, 0, [](int a, int b){return a+b;});
    for(int i = n; i >= 0; i--){
        int x = encode[s[i]];
        int cnt = st.query(x, x+1);
        ans += st.query(x, m);
        st.update(x, cnt+1);
    }
    cout << ans << endl;

    return 0;
}