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;
using ll = long long;
using Graph = vector<vector<int>>;
using WGraph = vector<vector<pair<int, ll>>>;

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

constexpr int dx[4] = {-1, 0, 0, 1}, dy[4] = {0, -1, 1, 0};
constexpr int INF = 1e9;
constexpr int MOD = 1e9 + 7;
constexpr long long LINF = 1e18;
constexpr double EPS = 1e-10;
constexpr double PI = M_PI;

template<int mod>
class ModInt {
    private:
        long long val;
    public:
        constexpr ModInt(const long long v = 0) : val(v%mod) { if (val < 0) val += mod; }
        constexpr ModInt(const ModInt &v) : val(v.val) {}
        constexpr ModInt &operator=(const long long v) { val = v; return *this; }
        constexpr ModInt &operator=(const ModInt &v) { if (this != &v) val = v.val; return *this; }
        constexpr ModInt operator+() const { return ModInt(val); }
        constexpr ModInt operator-() const { return ModInt(-val); }
        constexpr ModInt operator+(const ModInt &v) const { return ModInt(*this) += v; }
        constexpr ModInt operator-(const ModInt &v) const { return ModInt(*this) -= v; }
        constexpr ModInt operator*(const ModInt &v) const { return ModInt(*this) *= v; }
        constexpr ModInt operator/(const ModInt &v) const { return ModInt(*this) /= v; }
        constexpr ModInt &operator+=(const ModInt &v) { val += v.val; if (val >= mod) val -= mod; return *this; }
        constexpr ModInt &operator-=(const ModInt &v) { val -= v.val; if (val < 0) val += mod; return *this; }
        constexpr ModInt &operator*=(const ModInt &v) { val *= v.val; if (val >= mod) val %= mod; return *this; }
        constexpr ModInt &operator/=(const ModInt &v) { val *= v.inverse().val; if (val >= mod) val %= mod; return *this; }
        constexpr ModInt &operator++() { ++val; if (val >= mod) val -= mod; return *this; }
        constexpr ModInt &operator--() { --val; if (val < 0) val += mod; return *this; }
        constexpr ModInt operator++(int) { ModInt tmp(*this); operator++(); return tmp; }
        constexpr ModInt operator--(int) { ModInt tmp(*this); operator--(); return tmp; }
        constexpr bool operator==(const ModInt &v) const { return val == v.val; }
        constexpr bool operator!=(const ModInt &v) const { return !(*this == v); }
        friend std::istream &operator>>(std::istream &s, ModInt &v) { long long tmp; s >> tmp; v = ModInt(tmp); return s; }
        friend std::ostream &operator<<(std::ostream &s, const ModInt &v) { return s << v.val; }
        constexpr ModInt inverse() const {
            long long n = val, res = 1;
            while (n > 1) {
                res *= (mod - mod / n);
                res %= mod;
                n = mod % n;
            }
            return ModInt(res);
        }
        friend constexpr ModInt modpow(ModInt v, long long n) {
            ModInt res(1);
            for ( ; n>0; n>>=1) {
                if (n & 1) res *= v;
                v *= v;
            }
            return res;
        }
};

using MInt = ModInt<998244353>;

void solve() {
    int n, s;
    cin >> n >> s;
    vector<int> a(n);
    for (int i=0; i<n; ++i) cin >> a.at(i);

    vector<vector<MInt>> dp(n+1, vector<MInt>(s+1, MInt(0)));
    dp.at(0).at(0) = 1;
    for (int i=1; i<n+1; ++i) {
        int cur = a.at(i-1);
        for (int j=0; j<s+1; ++j) {
            dp.at(i).at(j) += dp.at(i-1).at(j);
            if (j == cur && j == s) {
                dp.at(i).at(j) += dp.at(i-1).at(j-cur) * i * (n-i+1);
            } else if (j == cur) {
                dp.at(i).at(j) += dp.at(i-1).at(j-cur) * i;
            } else if (j > cur && j == s) {
                dp.at(i).at(j) += dp.at(i-1).at(j-cur) * (n-i+1);
            } else if (j > cur) {
                dp.at(i).at(j) += dp.at(i-1).at(j-cur);
            }
        }
    }
    cout << dp.at(n).at(s) << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);

    solve();

    return 0;
}