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>
using namespace std;
const int N = 300000;
int n;
int k;
int ai[N];
#define LL long long
LL ss[N], af[N], ans;

int tr[N];
void add(int t, int d) {for (; t <= n + 5; t += t & (-t)) tr[t] += d;}
int sum(int t) {int d = 0; for (; t; t -= t & (-t)) d += tr[t]; return d;}
int main()
{
    cin >> n >> k;
    for (int i = 1; i <= n; ++ i)
    {
        cin >> ai[i];
        ai[i] -= k;
        ss[i] = ss[i - 1] + ai[i];
        af[i] = ss[i];
    }
    sort(af, af + n + 1);
    int tot = unique(af, af + n + 1) - af;
    for (int i = 0; i <= n; ++ i)
        ss[i] = lower_bound(af, af + tot, ss[i]) - af + 1;
    add(ss[0], 1);
    for (int i = 1; i <= n; ++ i)
    {
        ans += sum(ss[i]);
        add(ss[i], 1);
    }
    cout << ans;
}