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)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
struct FenwickTree {
    seq: Vec<i64>,
}
#[allow(dead_code)]
impl FenwickTree {
    fn new(n: usize) -> FenwickTree {
        FenwickTree {
            seq: vec![0; n + 2],
        }
    }
    fn add(&mut self, index: usize, value: i64) {
        let mut index = (index + 1) as i32;
        while (index as usize) < self.seq.len() {
            self.seq[index as usize] += value;
            index += index & -index;
        }
    }
    // inclusive
    fn sum(&self, index: usize) -> i64 {
        let mut ret = 0;
        let mut index = (index + 1) as i32;
        while index > 0 {
            ret += self.seq[index as usize];
            index -= index & -index;
        }
        ret
    }
}

fn main() {
    let n = read::<usize>();
    let k = read::<i64>();
    let mut aseq = vec![0; n];
    let mut sums = vec![(0, 0); n + 1];
    for i in 0..n {
        aseq[i] = read::<i64>() - k;
        sums[i + 1].0 = sums[i].0 + aseq[i];
        sums[i + 1].1 = i + 1;
    }
    let mut ftree = FenwickTree::new(n + 10);
    sums.sort();
    let mut ans = 0;
    let mut index = 0;
    for &(v, pos) in sums.iter() {
        if pos == 0 || pos == n + 1 {
            continue;
        }
        while index <= n && sums[index].0 <= v {
            ftree.add(sums[index].1, 1);
            index += 1;
        }
        ans += ftree.sum(pos - 1);
    }
    println!("{}", ans);
}