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)]
use std::cmp::{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;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = 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<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

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();
    }
}

use self::modint::ModInt;
mod modint {
    use std;
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt(usize);
    impl ModInt {
        pub fn new(value: usize) -> Self {
            ModInt(value % Self::modulo())
        }
        fn modulo() -> usize {
            998244353
        }
    }
    impl std::ops::Add for ModInt {
        type Output = Self;
        fn add(self, other: Self) -> Self {
            let mut value = self.0 + other.0;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Add<usize> for ModInt {
        type Output = Self;
        fn add(self, other: usize) -> Self {
            let mut value = self.0 + other;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Sub for ModInt {
        type Output = Self;
        fn sub(self, other: Self) -> Self {
            let mut value = self.0;
            if value < other.0 {
                value += Self::modulo();
            }
            value -= other.0;
            ModInt::new(value)
        }
    }
    impl std::ops::Sub<usize> for ModInt {
        type Output = Self;
        fn sub(self, other: usize) -> Self {
            let mut value = self.0;
            if value < other {
                value += Self::modulo();
            }
            value -= other;
            ModInt::new(value)
        }
    }
    impl std::ops::Mul for ModInt {
        type Output = Self;
        fn mul(self, other: Self) -> Self {
            let value = self.0 * other.0 % Self::modulo();
            ModInt::new(value)
        }
    }
    impl std::ops::Mul<usize> for ModInt {
        type Output = Self;
        fn mul(self, other: usize) -> Self {
            let value = self.0 * other % Self::modulo();
            ModInt::new(value)
        }
    }
    impl std::ops::Div for ModInt {
        type Output = Self;
        fn div(self, other: Self) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other.0;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Div<usize> for ModInt {
        type Output = Self;
        fn div(self, other: usize) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt::new(value)
        }
    }
    impl std::ops::AddAssign for ModInt {
        fn add_assign(&mut self, other: Self) {
            *self = *self + other;
        }
    }
    impl std::ops::AddAssign<usize> for ModInt {
        fn add_assign(&mut self, other: usize) {
            *self = *self + other;
        }
    }
    impl std::ops::SubAssign for ModInt {
        fn sub_assign(&mut self, other: Self) {
            *self = *self - other;
        }
    }
    impl std::ops::SubAssign<usize> for ModInt {
        fn sub_assign(&mut self, other: usize) {
            *self = *self - other;
        }
    }
    impl std::ops::MulAssign for ModInt {
        fn mul_assign(&mut self, other: Self) {
            *self = *self * other;
        }
    }
    impl std::ops::MulAssign<usize> for ModInt {
        fn mul_assign(&mut self, other: usize) {
            *self = *self * other;
        }
    }
    impl std::ops::DivAssign for ModInt {
        fn div_assign(&mut self, other: Self) {
            *self = *self / other;
        }
    }
    impl std::ops::DivAssign<usize> for ModInt {
        fn div_assign(&mut self, other: usize) {
            *self = *self / other;
        }
    }
    impl std::fmt::Debug for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    impl std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}

fn solve() {
    let (n,s) = get!(usize, usize);
    let a = get!([usize]);

    let mut dp = vec![vec![ModInt::new(0); s+1];n+1];
    dp[0][0] = ModInt::new(1);
    let mut sum = ModInt::new(0);
    for i in 0..n {
        for e in 0..s+1 {
            let tmp = if a[i] > e {
                dp[i][e]
            } else {
                dp[i][e] + dp[i][e-a[i]]
            };
            dp[i+1][e] += tmp;
        }
        dp[i+1][0] += 1;
        sum += dp[i+1][s];
    }

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