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>

int main(){
    constexpr long long mod=998244353;
    int N,S;std::cin>>N>>S;
    using ll = long long;
    std::vector<std::vector<std::vector<ll>>> dp(N+1,std::vector<std::vector<ll>>(S+1,std::vector<ll>(3)));
    std::vector<int> A(N);
    for(int i=0;i<N;++i) std::cin>>A[i];
    dp[0][0][0]=1;
    for(int i=0;i<N;++i) for(int s=0;s<=S;++s){
        dp[i+1][s][0]=dp[i][s][0];
        dp[i+1][s][1]=dp[i][s][1];
        dp[i+1][s][2]=dp[i][s][2];
        if(s>=A[i]){
            dp[i+1][s][1]+=(i+1)*dp[i][s-A[i]][0]+dp[i][s-A[i]][1];
            dp[i+1][s][2]+=(N-i)*dp[i][s-A[i]][1]+(N-i)*(i+1)*dp[i][s-A[i]][0];
        }
        for(int j=0;j<3;++j) dp[i+1][s][j]%=mod;
    }
    std::cout<<dp[N][S][2]<<std::endl;
}