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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int S = sc.nextInt();
        int[] A = new int[N];
        int mod = 998244353;
        long[] ruiseki = new long[N+1];
        for (int i=0;i<N;i++) {
            A[i] = sc.nextInt();
            ruiseki[i+1] = ruiseki[i]+A[i];
        }

        long[][][] dp = new long[3][N+1][S+1];
        dp[0][0][0] = 1;
        for (int i=0;i<N;i++) {
            for (int j=0;j<=S;j++) {
                dp[0][i+1][j] = (dp[0][i+1][j]+dp[0][i][j])%mod;
                dp[1][i+1][j] = (dp[1][i+1][j]+dp[1][i][j])%mod;
                dp[2][i+1][j] = (dp[2][i+1][j]+dp[2][i][j])%mod;
                if (j+A[i]<=S) {
                    if (j+A[i]!=S) {
                        dp[1][i+1][j+A[i]] = (dp[1][i+1][j+A[i]]+dp[0][i][j]*(i+1)%mod)%mod;
                    } else {
                        dp[2][i+1][j+A[i]] = (dp[2][i+1][j+A[i]]+dp[0][i][j]*(i+1)*(N-i)%mod)%mod;
                    }
                    if (j+A[i]!=S) {
                        dp[1][i+1][j+A[i]] = (dp[1][i+1][j+A[i]]+dp[1][i][j])%mod;
                    } else {
                        dp[2][i+1][j+A[i]] = (dp[2][i+1][j+A[i]]+dp[1][i][j]*(N-i)%mod)%mod;
                    }
                }
            }
        }
        System.out.println(dp[2][N][S]);
    }
}