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 $998244353$.