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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline

def main():
    n, s = map(int, input().split())
    a = list(map(int, input().split()))
    mod = 998244353
    
    dp0 = [[0]*(s+1) for _ in range(n+1)]
    dp1 = [[0]*(s+1) for _ in range(n+1)]
    dp2 = [[0]*(s+1) for _ in range(n+1)]
    dp0[0][0] = 1
    
    for i in range(n):
        for j in range(s+1):
            dp0[i+1][j] += dp0[i][j]
            dp1[i+1][j] += dp1[i][j]
            dp2[i+1][j] += dp2[i][j]
            
            
            if a[i]+j <= s:
                dp1[i+1][j+a[i]] += dp0[i][j] * (i+1)
                dp2[i+1][j+a[i]] += dp0[i][j] * (i+1) * (n-i)
                
                dp1[i+1][j+a[i]] += dp1[i][j]
                dp2[i+1][j+a[i]] += dp1[i][j] * (n-i)
                
            dp0[i+1][j] %= mod
            dp1[i+1][j] %= mod
            dp2[i+1][j] %= mod
                
    print(dp2[n][s])
    
    
if __name__ == "__main__":
    main()