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 unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
//typedef vector<vector<ll>> Graph;

//const ll mod = 1e9 + 7;
const ll mod = 998244353;

#define REP(i,n) for(ll i=0;i<(ll)n;i++)
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define spa << " " <<
#define fi first
#define se second

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }

template<class S, class T> ostream& operator << (ostream& os, const pair<S, T> v){
os << "(" << v.first << ", " << v.second << ")"; return os;
}
template<class T> ostream& operator << (ostream& os, const vector<T> v){
for(int i = 0; i < (int)v.size(); i++){if(i > 0){os << " ";} os << v[i];} return os;
}
template<class T> ostream& operator << (ostream& os, const vector<vector<T>> v){
for(int i = 0; i < (int)v.size(); i++){if(i > 0){os << endl;} os << v[i];} return os;
}

template<typename T> void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++)
{cerr<<v[i][0];for(ll j=1;j<w;j++)cerr spa v[i][j];cerr<<endl;}};
template<typename T> void debug(vector<T>&v,ll n){if(n!=0)cerr<<v[0];
for(ll i=1;i<n;i++)cerr spa v[i];
cerr<<endl;};

string num2bit(ll num, ll len){
    string bit = "";
    REP(i, len){
    bit += char('0'+(num>>i & 1));
    }
    return bit;
}

template <std::uint_fast64_t Modulus> class modint {
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};
using mint = modint<mod>;

mint dp[3030][3030][3];

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll N, S;
    cin >> N >> S;
    vector<ll> A(N);
    REP(i, N) cin >> A[i];

    REP(i, 3030)REP(j, 3030)REP(k, 3) dp[i][j][k] = 0;
    dp[0][0][0] = 1;

    REP(i, N){
        REP(j, S+1){
            dp[i+1][j][0] += dp[i][j][0];
            dp[i+1][j][1] += dp[i][j][0];
            if(j+A[i]<=S) dp[i+1][j+A[i]][1] += dp[i][j][0];
            dp[i+1][j][2] += dp[i][j][0];
            if(j+A[i]<=S) dp[i+1][j+A[i]][2] += dp[i][j][0];

            dp[i+1][j][1] += dp[i][j][1];
            if(j+A[i]<=S) dp[i+1][j+A[i]][1] += dp[i][j][1];
            dp[i+1][j][2] += dp[i][j][1];
            if(j+A[i]<=S) dp[i+1][j+A[i]][2] += dp[i][j][1];

            dp[i+1][j][2] += dp[i][j][2];
        }
    }

    cout << dp[N][S][2].value() << endl;

    return 0;
}