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<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define LL long long
using namespace std;
const int maxn=2e7+10;
const LL inf=1e17;
LL x[maxn];
struct AC
{
    struct zp
    {
        int lson,rson;
        LL sum;
    }tree[maxn];
    int cont,root;
    void init()
    {
        cont=0;
        root=-1;
    }
    int newnode()
    {
        tree[cont].lson=tree[cont].rson=-1;
        tree[cont].sum=0;
        cont++;
        return cont-1;
    }
    void update(int &k,LL l,LL r,LL num)
    {
        if(k==-1) k=newnode();
        tree[k].sum++;
        if(l==r) return ;
        LL mid=(l+r)>>1;
        if(num<=mid)
            update(tree[k].lson,l,mid,num);
        else
            update(tree[k].rson,mid+1,r,num);
    }
    LL query(int k,LL l,LL r,LL ql,LL qr)
    {
        if(k==-1) return 0;
        if(l==ql&&r==qr)
            return tree[k].sum;
        LL mid=(l+r)>>1;
        if(qr<=mid)
            return query(tree[k].lson,l,mid,ql,qr);
        else if(ql>mid)
            return query(tree[k].rson,mid+1,r,ql,qr);
        else
            return query(tree[k].lson,l,mid,ql,mid)+query(tree[k].rson,mid+1,r,mid+1,qr);
    }
}ac;
int main()
{
    int n;
    LL m;
    while(~scanf("%d%lld",&n,&m))
    {
        ac.init();
        for(int i=0;i<n;i++)
        {
            scanf("%lld",&x[i]);
            x[i]-=m;
        }
        for(int i=1;i<n;i++)
            x[i]+=x[i-1];
        ac.update(ac.root,-inf,inf,0);
        LL ans=0;
        for(int i=0;i<n;i++)
        {
            ans+=ac.query(ac.root,-inf,inf,-inf,x[i]);
            ac.update(ac.root,-inf,inf,x[i]);
        }
        printf("%lld\n",ans);
    }
}