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 <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>

using namespace __gnu_pbds;
using namespace std;

using ll = long long;

typedef
tree<
pair<ll,int>,
  null_type,
  less<pair<ll,int>>,
  rb_tree_tag,
  tree_order_statistics_node_update>
ordered_set;

ordered_set t;

int main()
{
  int N;
  ll K;
  scanf("%d %lld",&N,&K);

  t.insert({0,0});
  ll s = 0;
  ll ans = 0ll;
  for (int i=0;i<N;i++) {
    ll a;
    scanf("%lld",&a);
    s += a;
    ll v = s - (K * (ll)(i+1ll));
    ll here = (ll)(t.order_of_key({v, i+1}));
//    printf("i=%d, here=%lld\n",i,here);
    ans += here;
    t.insert({v, i+1});
  }
  printf("%lld\n",ans);
}