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 Kotlin (1.0.0) (judge verdict: Runtime Error)

fun main(args: Array<String>) {
    val mod = 998244353L

    val (N, S) = readInputLine().split(" ").map { it.toInt() }
    val AArr = readInputLine().split(" ").map { it.toInt() }.toIntArray()
    
    val dp = LongArray((N + 1) * (S + 1) * 3)
    dp[0] = 1L

    for (i in 0 until N) {
        for (j in 0..S) {
            dp[(i + 1) * (S + 1) * 3 + j * 3] += dp[i * (S + 1) * 3 + j * 3]
            dp[(i + 1) * (S + 1) * 3 + j * 3] %= mod
            dp[(i + 1) * (S + 1) * 3 + j * 3 + 1] += dp[i * (S + 1) * 3 + j * 3] + dp[i * (S + 1) * 3 + j * 3 + 1]
            dp[(i + 1) * (S + 1) * 3 + j * 3 + 1] %= mod
            dp[(i + 1) * (S + 1) * 3 + j * 3 + 2] += dp[i * (S + 1) * 3 + j * 3] + dp[i * (S + 1) * 3 + j * 3 + 1] + dp[i * (S + 1) * 3 + j * 3 + 2]
            dp[(i + 1) * (S + 1) * 3 + j * 3 + 2] %= mod

            if (j + AArr[i] <= S) {
                dp[(i + 1) * (S + 1) * 3 + (j + AArr[i]) * 3 + 1] += dp[i * (S + 1) * 3 + j * 3] + dp[i * (S + 1) * 3 + j * 3 + 1]
                dp[(i + 1) * (S + 1) * 3 + (j + AArr[i]) * 3 + 1] %= mod
                dp[(i + 1) * (S + 1) * 3 + (j + AArr[i]) * 3 + 2] += dp[i * (S + 1) * 3 + j * 3] + dp[i * (S + 1) * 3 + j * 3 + 1]
                dp[(i + 1) * (S + 1) * 3 + (j + AArr[i]) * 3 + 2] %= mod
            }
        }
    }

    println(dp[N * (S + 1) * 3 + S * 3 + 2])
}

fun readInputLine(): String {
    return readLine()!!
}