Problem Statement

Snuke the wizard has $N$ magical lamps numbered $1$ to $N$. The cost of the $i$-th lamp is $a_i$. Initially, none of the lamps are lit.

Snuke has an integer value called MP, which is initially $X$. When Snuke lights a lamp with cost $x$, his MP decreases by $x$. Each time Snuke lights one lamp, the cost of all lamps with cost at least $1$ decreases by $1$.

There are $N!$ possible orders to light the lamps. Find the number, modulo $998244353$, of such orders where MP never becomes negative.

Constraints

• $1 \le N \le 100$
• $0 \le a_i \le 10^{9}$
• $0 \le X \le 10^9$
• All input values are integers.

Input

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

N X
a_1 a_2 \dots a_N

Output

Print the answer.