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)

fn main() {
    const MOD: usize = 998244353;
    let mut line = String::new();
    std::io::stdin().read_line(&mut line);
    let ns: Vec<usize> = line.split_whitespace().map(|a| a.parse().unwrap()).collect();
    let s = (ns[1]);
    line = String::new();
    std::io::stdin().read_line(&mut line);
    let a: Vec<usize> = line.split_whitespace().map(|a| a.parse().unwrap()).collect();
    let n = a.len();
    let mut dp = vec![0; s + 1];
    dp[0] = 1;
    for &ai in &a {
        for j in (0 .. dp.len()).rev() {
            if j + ai < s {
                dp[j + ai] = (dp[j + ai] + dp[j]) % MOD;
            } else if j + ai == s {
                dp[j + ai] = (dp[j + ai] + dp[j] * (n - dp[0] + 1)) % MOD;
            }
        }
        dp[0] += 1;
    }
    println!("{}", dp[s]);
}