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:
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.141592653589793238462643383279;
const vector<ll>four{0,1,0,-1,0};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto &i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
inline ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
inline ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
template<class T> inline T min(const vector<T> &v){ return *min_element(range(v)); }
inline char min(const string &v){ return *min_element(range(v)); }
template<class T> inline T max(const vector<T> &v){ return *max_element(range(v)); }
inline char max(const string &v){ return *max_element(range(v)); }
inline ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
template<class T> inline bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> inline bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } return 0; }
template<class T> unordered_map<T, ll> press(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T, ll> press_map(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin >> a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ for(auto&& i : a) print(i); }
template<class T> inline void print(const vector<T> &vec);
template<class T, size_t size> inline void print(const array<T, size> &vec);
template<class T, class L> inline void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> inline void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> inline void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> inline void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline void err(){ putchar('\n'); }
template<class T> inline void err(const T &t){ print(t); putchar('\n'); }
template<class Head, class... Tail> inline void err(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); }
#else
template<class... T> inline void err(const T&... t){}
#endif
inline int first(bool i = true){ return out(i?"first":"second"); }
inline int yes(bool i = true){ return out(i?"yes":"no"); }
inline int Yes(bool i = true){ return out(i?"Yes":"No"); }
inline int No(){ return out("No"); }
inline int YES(bool i = true){ return out(i?"YES":"NO"); }
inline int NO(){ return out("NO"); }
inline int Yay(bool i = true){ return out(i?"Yay!":":("); }
inline int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
inline int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
inline void Case(ll i){ printf("Case #%lld: ", i); }


template<class T>
struct SegmentTree{
    virtual T f(const T&, const T&) const = 0;
    ll size = 1, rank = 0, expected_size;
    vector<T> data;
    const T def_value;
    SegmentTree(ll n, const T& def_value): def_value(def_value), expected_size(n){
        while(size < expected_size){
            size *= 2;
            rank++;
        }
        data.assign(size * 2, def_value);
    }
    SegmentTree(const vector<T>& v, const T& def_value): def_value(def_value), expected_size(v.size()){
        while(size < expected_size){
            size *= 2;
            rank++;
        }
        data.assign(size * 2, def_value);
        for(ll i = 0; i < v.size(); i++) data[size + i] = v[i];
        // for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
    T operator[](ll at) const {
        return data[size + at];
    }
    void update(ll at){
        while(at /= 2) data[at] = f(data[at * 2], data[at * 2 + 1]);
    }
    void set(ll at, const T& val){
        at += size;
        data[at] = val;
        update(at);
    }
    void add(ll at, const T& val){
        at += size;
        data[at] += val;
        update(at);
    }
    T get(ll l, ll r) const {
        T L = def_value, R = def_value;
        l += size; r += size;
        for(; l < r; l /= 2, r /= 2){
            if(l & 1) L = f(L, data[l++]);
            if(r & 1) R = f(data[--r], R);
        }
        return f(L, R);
    }
    template<class F> ll find_last(const F& check, ll l = 0) const { // max x  s.t. check(get(l, x)) == true
        if(l == expected_size) return expected_size;
        ll height = 0, at = l + size;
        T val = def_value;
        for(; height <= rank; height++) if(at >> height & 1){
            T val2 = f(val, data[at >> height]);
            if(check(val2)){
                at += 1 << height;
                if(at == size * 2) return expected_size;
                val = val2;
            }
            else break;
        }
        for(; height--; ){
            T val2 = f(val, data[at >> height]);
            if(check(val2)){
                at += 1 << height;
                val = val2;
            }
        }
        return min(at - size, expected_size);
    }
    template<class F> ll find_first(const F& check, ll r) const { // min x  s.t. check(get(x, r)) == true
        if(!r) return 0;
        ll height = 0, at = r + size;
        T val = def_value;
        for(; height <= rank; height++) if(at >> height & 1){
            T val2 = f(val, data[at >> height ^ 1]);
            if(check(val2)){
                at -= 1 << height;
                if(!at) return 0;
                val = val2;
            }
            else break;
        }
        for(; height--; ){
            T val2 = f(val, data[(at >> height) - 1]);
            if(check(val2)){
                at -= 1 << height;
                val = val2;
            }
        }
        return at - size;
    }
    void clear(){
        for(auto& i : data) i = def_value;
    }
};
template<class T>
struct RmQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return min(a, b);}
    RmQ(ll n, const T& def_value) : SegmentTree<T>(n, def_value){}
    RmQ(const vector<T>& v, const T& def_value) : SegmentTree<T>(v, def_value){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
template<class T>
struct RMQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return max(a, b);}
    RMQ(ll n, const T& def_value) : SegmentTree<T>(n, def_value, [](T a, T b){return max(a, b);}){}
    RMQ(const vector<T>& v, const T& def_value) : SegmentTree<T>(v, def_value, [](T a, T b){return max(a, b);}){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
template<class T>
struct RSQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return a + b;}
    RSQ(ll n, const T& def_value = T()) : SegmentTree<T>(n, def_value){}
    RSQ(const vector<T>& v, const T& def_value = T()) : SegmentTree<T>(v, def_value){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
signed main(){
    LL(n,k);
    VEC(ll,a,n);
    each(i,a)i-=k;
    vec(ll,s,n+1);
    rep(n)s[i+1]=s[i]+a[i];
    auto pr=press(s);
    RSQ<ll>seg(pr.size());
    ll ans=0;
    each(i,s){
        ans+=seg.get(0,i+1);
        seg.add(i,1);
    }
    out(ans);
}