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 <map>
#include <set>
#include <queue>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <fstream>
#include <cassert>
#include <cstring>
#include <unordered_set>
#include <unordered_map>
#include <numeric>
#include <ctime>
#include <bitset>
#include <complex>
#include <chrono>
#include <random>
#include <functional>

using namespace std;

#define int long long

struct Fenwick {
	int n;
	vector<int> f;

	Fenwick(int n_) {
		n = n_;
		f.resize(n);
	}

	int get(int x) {
		int res = 0;
		for (int i = x; i >= 0; i = (i & (i + 1)) - 1) {
			res += f[i];
		}
		return res;
	}

	void add(int x, int v) {
		for (int i = x; i < n; i = (i | (i + 1))) {
			f[i] += v;
		}
	}
};

signed main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	int n, k;
	cin >> n >> k;
	vector<int> a(n);
	for (auto &t : a) {
		cin >> t;
	}
	vector<int> ps(n + 1);
	for (int i = 0; i < n; i++) {
		ps[i + 1] = ps[i] + a[i];
	}
	vector<int> v(n + 1);
	for (int i = 0; i <= n; i++) {
		v[i] = k * i - ps[i];
		v[i] *= -1;
	}
	{
		vector<int> seen = v;
		sort(seen.begin(), seen.end());
		seen.resize(unique(seen.begin(), seen.end()) - seen.begin());
		for (auto &t : v) {
			t = lower_bound(seen.begin(), seen.end(), t) - seen.begin();
		}
	}
	int ans = 0;
	Fenwick f(n + 1);
	for (int i = 0; i <= n; i++) {
		ans += f.get(v[i]);
		f.add(v[i], 1);
	}
	cout << ans << endl;
}