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: Time Limit Exceeded)

use std::io::{Read, StdinLock};
use std::iter::{FromIterator, Iterator};
use std::str::{FromStr};
use std::string::String;

macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

pub fn read_bytes<T: FromIterator<char>>(s: &mut StdinLock) -> T {
    s.bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<T>()
}

pub fn reads(s: &mut StdinLock) -> String {
    read_bytes::<String>(s)
}

pub fn read<T: FromStr>(s: &mut StdinLock) -> T {
    reads(s).parse().ok().unwrap()
}

//==============================================================================
//
// Problem specific code
//
//==============================================================================

const M: i64 = 998244353;

fn sum_f(n: usize, s: usize, ais: &Vec<usize>, l: usize) -> i64 {
    (l..n).fold((0, vec![0i64; s + 1]), |(tot, mut dp), i| {
        dp[0] = 1;  // 和 0 を作るのは空集合ただ1通りのみ
        let dp_ = (0..(s + 1)).map(|w| {
            if w < ais[i] { dp[w] } else { (dp[w - ais[i]] + dp[w]) % M }
        }).collect::<Vec<_>>();
        (tot + dp_[s], dp_)
    }).0
}

fn main() {
    let sin = std::io::stdin();
    let mut sin = sin.lock();

    let n: usize = read(&mut sin);
    let s: usize = read(&mut sin);
    let ais: Vec<usize> = (0..n).map(|_| read(&mut sin)).collect();

    let ans = (0..n).fold(0i64, |a, l| (a + sum_f(n, s, &ais, l)) % M);
    println!("{}", ans);
}