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)

N,S = map(int,input().split())
A = list(map(int,input().split()))
MOD=998244353

#まだ左端を選択していない状態(状態 0)。この時は和が0の時1通りでそれ以外は0。
#左端は選択済みだけど右端は選択していない状態(状態 1)
#右端も選択済みの状態(状態 2)

dp = [[[0 for _ in range(3)] for _ in range(S+1)] for _ in range(N+1)]
dp[0][0][0] = 1
#i個目までで和がjとなる場合の数
ans = 0

for i in range(N):
  for j in range(S+1):
    #from 0
    #if j == 0: #j==0の時以外は基本0なのであってもなくても良い。
    dp[i+1][j][0] += dp[i][j][0]%MOD
    if j+A[i] <= S:# and j == 0: #j==0の時以外は基本0なのであってもなくても良い。
      dp[i+1][j+A[i]][1] += dp[i][j][0] * (i+1)%MOD
      dp[i+1][j+A[i]][2] += dp[i][j][0] * (i+1) * (N-i)%MOD
    #from 1
    dp[i+1][j][1] += dp[i][j][1]%MOD
    if j+A[i] <= S:
      dp[i+1][j+A[i]][1] += dp[i][j][1]%MOD
      dp[i+1][j+A[i]][2] += dp[i][j][1] * (N-i)%MOD
    #from 2
    dp[i+1][j][2] += dp[i][j][2]%MOD
#print(dp)MODDD
print(dp[N][S][2]%MOD)