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>
#define F first
#define S second
#define int long long
#define pii pair<int, int>
#define ins insert
#define sz size() 

using namespace std;

template<typename T>
using ordered_set = __gnu_pbds::tree<T,__gnu_pbds::null_type,std::less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;

ordered_set < pii > st;
const int maxn = 2e5+5;
int n, k, ans, a[maxn];

void Speed() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}

main(){
    Speed();
    cin >> n >> k;
    for(int i = 1; i <= n; ++ i) {
        cin >> a[i];
        a[i] -= k;
        a[i] += a[i - 1];
    }
    for(int i = 0; i <= n; ++ i) {
        int cnt = st.order_of_key({a[i] + 1, -1});
        ans += cnt;
        st.ins({a[i], i});
    }
    cout << ans;
}