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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/python3
import copy

r = 998244353

(n, s) = map(int, input().split())

a = list(map(int, input().split()))

# s => comb
itbl = {}
rtbl = {}

for i in range(n):
    ai = a[i]
    
    #itbl
    nitbl = copy.copy(itbl)
    if ai in nitbl:
        nitbl[ai] = (nitbl[ai] + i + 1) % r
    else:
        nitbl[ai] = i + 1

    for sk in itbl:
        if sk + ai in nitbl:
            nitbl[sk + ai] = (nitbl[sk + ai] + itbl[sk]) % r
        else:
            nitbl[sk + ai] = itbl[sk]

    #rtbl
    if ai in rtbl:
        rtbl[ai] += (i + 1) * (n - i)
    else:
        rtbl[ai] = (i + 1) * (n - i)

    for sk in itbl:
        if sk + ai in rtbl:
            rtbl[sk + ai] = (rtbl[sk + ai] + itbl[sk] * (n - i)) % r
        else:
            rtbl[sk + ai] = (itbl[sk] * (n - i)) % r
            
    itbl = nitbl
    
print(rtbl.get(s, 0))