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 Rust (1.15.1) (judge verdict: Accepted)

/**
*  _           _                 __                            _   _ _   _                                 _                    _                  _
* | |         | |               / /                           | | (_) | (_)                               | |                  (_)                | |
* | |__   __ _| |_ ___   ___   / /__ ___  _ __ ___  _ __   ___| |_ _| |_ ___   _____ ______ _ __ _   _ ___| |_ ______ ___ _ __  _ _ __  _ __   ___| |_ ___
* | '_ \ / _` | __/ _ \ / _ \ / / __/ _ \| '_ ` _ \| '_ \ / _ \ __| | __| \ \ / / _ \______| '__| | | / __| __|______/ __| '_ \| | '_ \| '_ \ / _ \ __/ __|
* | | | | (_| | || (_) | (_) / / (_| (_) | | | | | | |_) |  __/ |_| | |_| |\ V /  __/      | |  | |_| \__ \ |_       \__ \ | | | | |_) | |_) |  __/ |_\__ \
* |_| |_|\__,_|\__\___/ \___/_/ \___\___/|_| |_| |_| .__/ \___|\__|_|\__|_| \_/ \___|      |_|   \__,_|___/\__|      |___/_| |_|_| .__/| .__/ \___|\__|___/
*                                                  | |                                                                           | |   | |
*                                                  |_|                                                                           |_|   |_|
*
* https://github.com/hatoo/competitive-rust-snippets
*/
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
mod util {
    use std::fmt::Debug;
    use std::io::{stdin, stdout, BufWriter, StdoutLock};
    use std::str::FromStr;
    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }
    #[allow(dead_code)]
    pub fn chars() -> Vec<char> {
        line().chars().collect()
    }
    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
    #[allow(dead_code)]
    pub fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>) -> ()>(f: F) {
        let out = stdout();
        let writer = BufWriter::new(out.lock());
        f(writer)
    }
}
#[allow(unused_macros)]
macro_rules ! get { ( $ t : ty ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . trim ( ) . parse ::<$ t > ( ) . unwrap ( ) } } ; ( $ ( $ t : ty ) ,* ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; let mut iter = line . split_whitespace ( ) ; ( $ ( iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) , ) * ) } } ; ( $ t : ty ; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ ( $ t : ty ) ,*; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ ( $ t ) ,* ) ) . collect ::< Vec < _ >> ( ) } ; ( $ t : ty ;; ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . split_whitespace ( ) . map ( | t | t . parse ::<$ t > ( ) . unwrap ( ) ) . collect ::< Vec < _ >> ( ) } } ; ( $ t : ty ;; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ;; ) ) . collect ::< Vec < _ >> ( ) } ; }
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

#[allow(dead_code)]
pub trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}
#[allow(dead_code)]
/// Segment Tree
pub struct SEG<M: Monoid> {
    n: usize,
    buf: Vec<M::T>,
}
impl<M: Monoid> SEG<M> {
    #[allow(dead_code)]
    pub fn new(n: usize) -> SEG<M> {
        SEG {
            n: n,
            buf: vec![M::id().clone(); 2 * n],
        }
    }
    #[allow(dead_code)]
    pub fn update(&mut self, k: usize, a: M::T) {
        let mut k = k + self.n;
        self.buf[k] = a;
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    pub fn add(&mut self, k: usize, a: &M::T) {
        let mut k = k + self.n;
        self.buf[k] = M::op(&self.buf[k], a);
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    fn query(&self, l: usize, r: usize) -> Option<M::T> {
        let combine = |resl, resr| match (resl, resr) {
            (Some(l), Some(r)) => Some(M::op(&l, &r)),
            (Some(l), None) => Some(l),
            (None, Some(r)) => Some(r),
            _ => None,
        };
        let mut vl = None;
        let mut vr = None;
        let mut l = l + self.n;
        let mut r = r + self.n;
        while l < r {
            if l & 1 == 1 {
                vl = combine(vl, Some(self.buf[l].clone()));
                l += 1;
            }
            if r & 1 == 1 {
                r -= 1;
                vr = combine(Some(self.buf[r].clone()), vr);
            }
            l >>= 1;
            r >>= 1;
        }
        combine(vl, vr)
    }
}

#[allow(dead_code)]
struct SUM;
impl Monoid for SUM {
    type T = i64;
    fn id() -> Self::T {
        0
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
}

fn solve() {
    let (n, k) = get!(usize, i64);
    let mut aa = get!(i64; n);

    for a in &mut aa {
        *a -= k;
    }

    let mut t = 0;
    let mut cc = vec![0];

    for &a in &aa {
        t += a;
        cc.push(t);
    }

    cc.sort();
    cc.dedup();

    let mut seg: SEG<SUM> = SEG::new(cc.len());

    let mut t = 0;
    for &a in &aa {
        t += a;
        let c = cc.binary_search(&t).unwrap();
        seg.add(c, &1);
    }

    let m = cc.len();
    let mut ans = seg.query(cc.binary_search(&0).unwrap(), m).unwrap();

    let mut t = 0;
    for &a in &aa {
        t += a;
        let c = cc.binary_search(&t).unwrap();
        seg.add(c, &(-1));

        ans += seg.query(c, m).unwrap_or(0);
    }

    println!("{}", ans);
}