Problem Statement

You are given a length-$N$ sequence of positive integers $A=(A _ 1,A _ 2,\ldots,A _ N)$ and a positive integer $M$.

Find the number of length-$N$ sequences of non-negative integers $x=(x _ 1,x _ 2,\ldots,x _ N)$ that satisfy the following condition:

• $\displaystyle\sum _ {i=1} ^ NA _ ix _ i\le M$

The number can be very large, so find it modulo $998244353$.

Constraints

• $1\le N\le100$
• $1\le A _ i\le100\ (1\le i\le N)$
• $1\le M\le10 ^ {18}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
A _ 1 A _ 2 \ldots A _ N

Output

Print the number, modulo $998244353$, of non-negative integer sequences that satisfy the condition.