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>
#define int long long
using namespace std;
const int mod = 998244353;

int dp[2][3005][3005];
int a[3005];
int n,k;

void add(int &a, int b)
{
    a += b;
    if (a >= mod) a %= mod;
}

int solve(bool start, int i, int sum)
{
    int &res = dp[start][i][sum];
    if (sum == k) return n - i + 2;
    if (sum > k || i > n) return 0;
    if (res != -1) return res;
    res = 0;
    add(res, solve(start, i + 1, sum));
    int num;
    if (start) num = solve(true, i + 1, sum + a[i]);
    else num = i * solve(true, i + 1, sum + a[i]);
    add(res, num);
    return res;
}

signed main()
{
    //freopen("file.inp","r",stdin);
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
    }
    memset(dp, -1, sizeof(dp));
    cout << solve(0, 1, 0);
    return 0;
}