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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
 
using namespace std;
using ll = long long;

void Main(){
    ll n, s, i, j;
    cin >> n >> s;
    vector<ll> a(n);
    for (i=0; i<n; i++){
        cin >> a.at(i);
    }
    vector<vector<ll>> t(n, vector<ll>(s+1));
    for (ll i=0; i<n; i++){
        t[i][0] = i+2;        
    }
    if (a[0] <= s){
        t[0][a[0]] = 1;
    }
    for (i=1; i<n; i++){
        for (j=1; j<s+1; j++){
            t[i][j] = t[i-1][j];
            if (j - a[i] >= 0){
                t[i][j] += t[i-1][j-a[i]];
            }
        }
    }
    ll sum = 0;
    for (vector<ll> v: t){
        // for (ll x : v){
        //     cout << x;
        // }
        // cout << endl;
        sum += v[s];
    }
    sum = sum % 998244353;
    cout << sum;
}

int main(void){
    std::cin.tie(nullptr);
	std::ios_base::sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
    Main();
}