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: Runtime Error)

use std::io::{self, BufRead};

fn dp(memo: &mut Vec<Vec<Vec<i32>>>, vs: &Vec<i32>, i: usize, j: usize, s: i32) -> i32{
  let m = memo[i][j][s as usize];
  if m >= 0 {
    m
  } else if i == j {
    if s == vs[j] || s == 0 {
      1
    } else {
      0
    }
  } else {
    let v = vs[j];
    let result = if s < v {
      dp(memo, vs, i, j - 1, s)
    } else {
      dp(memo, vs, i, j - 1, s - v) + dp(memo, vs, i, j - 1, s)
    };
    memo[i][j][s as usize] = result;
    result
  }
}

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let line = lines.next().unwrap().unwrap();
  let vs: Vec<usize> = line.split(' ').map(|x| x.parse().unwrap()).collect();
  let n = vs[0];
  let s = vs[1] as i32;
  let line = lines.next().unwrap().unwrap();
  let vs: Vec<i32> = line.split(' ').map(|x| x.parse().unwrap()).collect();

  let mut memo = vec![vec![vec![-1; (s+1) as usize]; n]; n];
  let mut sum = 0;

  for i in 0..n {
    for j in i..n {
      let result = dp(&mut memo, &vs, i, j, s);
      sum += result;
    }
  }

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