Problem: K Average Ranges

Given the sequence a_1, a_2, .., a_N.

How many intervals in this sequence have an average value of K or more and a length of 1 or more?

input


N K
a_1 a_2 ... a_N


output

Output the answer.

Constraint

* 1 \ leq N \ leq 10 ^ 5
* 1 \ leq K \ leq 10 ^ 9
* 1 \ leq a_i \ leq 10 ^ 9



Input example


6 6
8 6 9 1 2 1


Output example


7






Example

Input

6 6
8 6 9 1 2 1


Output

7

Solution (in CPP):

Solution:
// #define _GLIBCXX_DEBUG // for STL debug (optional)
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>
using namespace std;
using ll = long long int;
using int64 = long long int;
 
template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}
 
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const int INF = 1LL << 29;
const ll LONGINF = 1LL << 60;
const ll MOD = 1000000007LL;

// @category セグメント木 (Segment Tree)
// @title セグメント木 (Segment Tree)
// 抽象 SegmentTree (0-indexed・一点更新・区間取得)
template <typename MonoidType>
struct SegmentTree {
    using Function = function< MonoidType(MonoidType, MonoidType) >;

    // node, identity element
    int n;
    vector<MonoidType> node;
    MonoidType E0;

    // update / combine function
    Function upd_f, cmb_f;

    void build(int m, vector<MonoidType> v = vector<MonoidType>()) {
        if(v != vector<MonoidType>()) m = v.size();
        n = 1; while(n < m) n *= 2;

        node = vector<MonoidType>(2*n-1, E0);
        if(v != vector<MonoidType>()) {
            for(int i=0; i<m; i++) {
                node[n-1+i] = v[i];
            }
            for(int i=n-2; i>=0; i--) {
                node[i] = cmb_f(node[2*i+1], node[2*i+2]);
            }
        }
    }

    // initialize
    SegmentTree() {}
    SegmentTree(int n_, MonoidType E0_,
                Function upd_f_, Function cmb_f_,
                vector<MonoidType> v = vector<MonoidType>()) :
        E0(E0_), upd_f(upd_f_), cmb_f(cmb_f_) {
        build(n_, v);
    }

    // update k-th element (applied value: x)
    void update(int k, MonoidType x) {
        k += n - 1;
        node[k] = upd_f(node[k], x);
        while(k > 0) {
            k = (k - 1) / 2;
            node[k] = cmb_f(node[2*k+1], node[2*k+2]);
        }
    }

    // range query for [a, b)
    // 非再帰のアイデア: http://d.hatena.ne.jp/komiyam/20131202/1385992406
    MonoidType query(int a, int b) {
        MonoidType vl = E0, vr = E0;
        for(int l=a+n, r=b+n; l<r; l>>=1, r>>=1) {
            if(l & 1) vl = cmb_f(vl, node[(l++)-1]);
            if(r & 1) vr = cmb_f(node[(--r)-1], vr);
        }
        return cmb_f(vl, vr);
    }
};


int main() {
    int N, K; cin >> N >> K;
    vector<ll> A(N);
    for(int i=0; i<N; i++) cin >> A[i], A[i] -= K;

    vector<ll> S(N+1);
    for(int i=0; i<N; i++) S[i+1] = S[i] + A[i];

    vector<ll> M = S;
    sort(M.begin(), M.end());
    M.erase(unique(M.begin(), M.end()), M.end());

    int SZ = M.size();
    SegmentTree<int> seg(SZ, 0,
                         [](int a, int b) { return a + b; },
                         [](int a, int b) { return a + b; });
    ll ans = 0;
    {
        int k = lower_bound(M.begin(), M.end(), 0) - M.begin();
        seg.update(k, 1);
    }
    for(int i=0; i<N; i++) {
        int k = lower_bound(M.begin(), M.end(), S[i+1]) - M.begin();
        ans += seg.query(0, k+1);
        seg.update(k, 1);
    }
    cout << ans << endl;
    return 0;
}