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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int M=200010;

struct Node *null;
struct Node
{
	ll v;int t;
	Node *lch,*rch;
	Node() {}
	Node(ll _v) : v(_v),t(1),lch(null),rch(null) {}
	bool isbad() {return lch->t*3>t*2+10||rch->t*3>t*2+10;}
	void update() {t=lch->t+rch->t+1;}
}*root,*vec[M];
int tot;

void dfs(Node *p)
{
	if(p->lch!=null) dfs(p->lch);
	vec[tot++]=p;
	if(p->rch!=null) dfs(p->rch);
}

Node *divide(int l,int r)
{
	if(l==r) return null;
	int mi=l+r>>1;
	Node *p=vec[mi];
	p->lch=divide(l,mi);
	p->rch=divide(mi,r);
	p->update();
	return p;
}

void rebuild(Node *&p)
{
	tot=0;
	dfs(p);
	p=divide(0,tot);
}

Node **top;
void insert(Node *&p,ll v)
{
	if(p==null)
	{
		p=new Node(v);
		top=&null;
		return;
	}
	if(v<p->v) insert(p->lch,v);
	else insert(p->rch,v);
	p->update();
	if(p->isbad()) top=&null;
	if(p==root&&*top!=null) rebuild(*top);
}

int query(Node *p,int v)
{
	if(p==null) return 0;
	if(v<p->v) return query(p->lch,v);
	return p->lch->t+1+query(p->rch,v);
}

int n,k;
ll a[M],ans;

int main()
{
	ios::sync_with_stdio(false);
	cin>>n>>k;
	for(int i=1;i<=n;i++)
		cin>>a[i],a[i]-=k;
	for(int i=1;i<=n;i++)
		a[i]+=a[i-1];
	root=null=new Node;
	insert(root,0);
	for(int i=1;i<=n;i++)
	{
		ans+=query(root,a[i]);
		insert(root,a[i]);
	}
	cout<<ans;
	return 0;
}