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;

#define ll long long int

ll MOD;
ll dp[3002][3002][2];

ll f(vector<ll>& a, ll i, ll s, bool flag) {
    if(s == 0) {
        return (ll)(a.size() + 1 - i);
    }
    if(s < 0 || i == a.size())
        return 0ll;
    if(dp[i][s][flag] != -1)
        return dp[i][s][flag];
    ll ans = 0;
    if(!flag) {
        ans += f(a, i + 1, s, flag);
        ans += (ll)(i + 1) * f(a, i + 1, s - a[i], !flag);
    }
    else {
        ans += f(a, i + 1, s, flag);
        ans += f(a, i + 1, s - a[i], flag);
    }
    return dp[i][s][flag] = ans % MOD;
}

int main() {
  MOD = 998244353;
  ll n, s;
  memset(dp, -1, sizeof dp);
  cin >> n >> s;
  vector<ll> a(n);
  for(ll i = 0; i < n; i++)
    cin >> a[i];
  cout << f(a, 0, s, 0);
}