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)

use std::cmp::min;
use std::io::stdin;

fn main() {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    let mut itr = s.split_whitespace().map(|e| e.parse::<usize>().unwrap());
    let n = itr.next().unwrap();
    let k = itr.next().unwrap();
    let m = 998244353;
    let mut s = String::new();
    stdin().read_line(&mut s).ok();

    let v: Vec<usize> = s
        .split_whitespace()
        .map(|e| e.parse::<usize>().unwrap())
        .collect();

    let mut a = vec![0; k + 1];
    let mut ans = 0;
    for i in 0..n {
        a[0] += 1;
        let mut a2 = vec![0; k + 1];
        for j in 0..k + 1 {
            a2[j] = (a2[j] + a[j]) % m;
            if j + v[i] <= k {
                a2[j + v[i]] = (a2[j + v[i]] + a[j]) % m;
            }
        }

        a = a2;

        ans = (ans + a[k]) % m;
    }

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