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: Accepted)

import sys

input = sys.stdin.readline
sys.setrecursionlimit(100000)
# mod = 10 ** 9 + 7
mod = 998244353


def read_values():
    return map(int, input().split())


def read_index():
    return map(lambda x: int(x) - 1, input().split())


def read_list():
    return list(read_values())


def read_lists(N):
    return [read_list() for n in range(N)]


class V:
    def __init__(self, f, v=None):
        self.f = f
        self.v = v

    def __str__(self):
        return str(self.v)

    def ud(self, n):
        if n is None:
            return

        if self.v is None:
            self.v = n
            return
        self.v = self.f(self.v, n)


def main():
    N, S = read_values()
    A = read_list()

    dp = [(0, 0, 0) for _ in range(S + 1)]
    dp[0] = (1, 1, 1)

    for a in A:
        for s in range(S, -1, -1):
            d1 = dp[s][0]
            d2 = (dp[s][1] + (0 if s - a < 0 else dp[s - a][1]) + d1) % mod
            d3 = (dp[s][2] + (0 if s - a < 0 else dp[s - a][1]) + d2) % mod
            dp[s] = (d1, d2, d3)

    print((dp[S][2] - dp[S][1]) % mod)


if __name__ == "__main__":
    main()