Problem:
Score : 600 points

Problem Statement

Given are a sequence of N integers A_1, A_2, \ldots, A_N and a positive integer S.

For a pair of integers (L, R) such that 1\leq L \leq R \leq N, let us define f(L, R) as follows:

f(L, R) is the number of sequences of integers (x_1, x_2, \ldots , x_k) such that L \leq x_1 < x_2 < \cdots < x_k \leq R and A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.

Find the sum of f(L, R) over all pairs of integers (L, R) such that 1\leq L \leq R\leq N. Since this sum can be enormous, print it modulo 998244353.

Constraints

All values in input are integers.

1 \leq N \leq 3000

1 \leq S \leq 3000

1 \leq A_i \leq 3000

Input

Input is given from Standard Input in the following format:

N S
A_1 A_2 ... A_N

Output

Print the sum of f(L, R), modulo 998244353.

Sample Input 1

3 4
2 2 4

Sample Output 1

5

The value of f(L, R) for each pair is as follows, for a total of 5.

f(1,1) = 0

f(1,2) = 1 (for the sequence (1, 2))

f(1,3) = 2 (for (1, 2) and (3))

f(2,2) = 0

f(2,3) = 1 (for (3))

f(3,3) = 1 (for (3))

Sample Input 2

5 8
9 9 9 9 9

Sample Output 2

0

Sample Input 3

10 10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

152

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! inc {
    ($x:expr, $dx:expr) => {{
        let a = $dx;
        $x = $x + a;
    }}
}

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 998244353;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let s: usize = sc.cin();
    let xs: Vec<usize> = sc.vec(n);

    let mut dp = vec![vec![ModInt::new(0, M); 4000]; 4000];
    let mut ans = ModInt::new(0, M);

    for i in 0..n {
        if i == 0 {
            dp[0][xs[0]] += 1;
        } else {
            dp[i][xs[i]] += (i + 1) as i64;
            for k in 0..s+1 {
                inc!(dp[i][k], dp[i-1][k]);
                if k >= xs[i] {
                    inc!(dp[i][k], dp[i-1][k - xs[i]]);
                }
            }
        }
        ans += dp[i][s];
    }
    put!(ans);
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}

#[derive(Debug, PartialEq, Eq, Clone, Copy)]
struct ModInt { res: i64, md: i64 }

impl ModInt {
    fn new(res: i64, md: i64) -> Self {
        ModInt { res: res, md: md }
    }
    fn inv(self) -> Self {
        fn exgcd(r0: i64, a0: i64, b0: i64, r: i64, a: i64, b: i64)
                -> (i64, i64, i64) {
            if r > 0 {
                exgcd(r, a, b, r0 % r, a0 - r0 / r * a, b0 - r0 / r * b)
            } else {
                (a0, b0, r0)
            }
        }
        let (a, _, r) = exgcd(self.res, 1, 0, self.md, 0, 1);
        if r != 1 { panic!("{:?} has no inverse!", self); }
        ModInt::new(((a % self.md) + self.md) % self.md, self.md)
    }
    fn pow(self, n: i64) -> Self {
        if n < 0 {
            self.pow(-n).inv()
        } else if n == 0 {
            ModInt::new(1, self.md)
        } else if n == 1 {
            self
        } else {
            let mut x = (self * self).pow(n / 2);
            if n % 2 == 1 { x *= self }
            x
        }
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.res)
    }
}
impl std::ops::Neg for ModInt {
    type Output = Self;
    fn neg(self) -> Self {
        if self.res == 0 { return self }
        ModInt { res: self.md - self.res, md: self.md }
    }
}
impl std::ops::Add<i64> for ModInt {
    type Output = Self;
    fn add(self, other: i64) -> Self {
        let res = if self.res + other >= self.md {
            self.res + other - self.md
        } else {
            self.res + other
        };
        ModInt { res: res, md: self.md }
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: ModInt) -> Self {
        self + other.res
    }
}
impl std::ops::Add<ModInt> for i64 {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        other + self
    }
}
impl std::ops::AddAssign<i64> for ModInt {
    fn add_assign(&mut self, other: i64) {
        self.res += other;
        if self.res >= self.md {
            self.res -= self.md;
        }
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: ModInt) {
        *self += other.res;
    }
}
impl std::ops::Sub<i64> for ModInt {
    type Output = Self;
    fn sub(self, other: i64) -> Self {
        let res = if self.res < other {
            self.res + self.md - other
        } else {
            self.res - other
        };
        ModInt { res: res, md: self.md }
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: ModInt) -> Self {
        self - other.res
    }
}
impl std::ops::Sub<ModInt> for i64 {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        -other + self
    }
}
impl std::ops::SubAssign<i64> for ModInt {
    fn sub_assign(&mut self, other: i64) {
        if self.res < other {
            self.res = self.res - other + self.md;
        } else {
            self.res -= other;
        }
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: ModInt) {
        *self -= other.res;
    }
}
impl std::ops::Mul<i64> for ModInt {
    type Output = Self;
    fn mul(self, other: i64) -> Self {
        ModInt { res: (self.res * other) % self.md, md: self.md }
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: ModInt) -> Self {
        self * other.res
    }
}
impl std::ops::Mul<ModInt> for i64 {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        other * self
    }
}
impl std::ops::MulAssign<i64> for ModInt {
    fn mul_assign(&mut self, other: i64) {
        self.res = (self.res * other) % self.md;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: ModInt) {
        *self *= other.res;
    }
}
impl std::ops::Div<i64> for ModInt {
    type Output = Self;
    fn div(self, other: i64) -> Self {
        self * ModInt::new(other, self.md).inv()
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: ModInt) -> Self {
        self * other.inv()
    }
}
impl std::ops::Div<ModInt> for i64 {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        other.inv() * self
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: ModInt) {
        self.res = (self.res * other.inv().res) % self.md;
    }
}
impl std::ops::DivAssign<i64> for ModInt {
    fn div_assign(&mut self, other: i64) {
        *self /= ModInt::new(other, self.md);
    }
}