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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
const ll MOD = 998244353;

ll add(ll x)
{
  return (x + MOD) % MOD;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);

    ll n, s, ans = 0;
    cin >> n >> s;
    vi dp(3010, 0);
    for (int  i =0 ; i < n; i++)
    {
        ll a;
        cin >> a;
        for (int j = s; j >= a; j--)
            dp[j] = add(dp[j] + dp[j - a]);    // add the number of sequences iteratively for each previous element  
        dp[0] += 1;
        dp[a] += 1;
        ans = add(dp[s] + ans);
    }
    cout << (ans + MOD) % MOD << endl;
    return 0;
}