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 <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
#define int long long
#define rep(i, n) for (signed i = 0; i < signed(n); i++)
#define REP(i, s, n) for (signed i = signed(s); i < signed(n); i++)
using namespace __gnu_pbds;
using namespace std;

using VV = vector<vector<int>>;
using V = vector<int>;
using P = pair<int, int>;
using IP = pair<int, P>;

template<typename T>
inline void input(vector<T>& v) { for (auto& x : v) cin >> x; }

signed main() {
    using key = pair<int, int>;
    tree<key,null_type,less<key>,rb_tree_tag,tree_order_statistics_node_update> tr;
	int N, K; cin >> N >> K;
	V v(N); input(v);
	V s(N + 1);
    int ans = 0;
    tr.insert(make_pair(0, -1ll));
	rep(i, N) {
		s[i + 1] = s[i] + v[i] - K;
        int num = tr.order_of_key(make_pair(s[i + 1], N));
        num = max(0ll, num);
        ans += num;
        tr.insert(make_pair(s[i + 1], (int)i));
	}
    cout << ans << endl;
}