Problem Statement

There are $M$ cells arranged in a horizontal row. SF-kun will place indistinguishable coins on these cells by repeating the following operation $0$ or more times.

• Let $x$ be the number of cells without a coin at the start of the operation.
• Specify an integer $i$ satisfying $1\le i\le N$ and $A_i\le x$. Here, you may specify an $i$ that was chosen in a previous operation again. (If no $i$ satisfies the condition, the operation cannot be performed.)
• Freely choose $A_i$ cells that do not have a coin yet. However, the leftmost cell among the cells without a coin must be chosen.
• Place a coin on every chosen cell.

Find the number of possible coin configurations after finishing the operations, modulo $998244353$.

Here, two coin configurations are considered different if there exists a cell that has a coin in exactly one of them.

Input

$N\ \ M$
$A_1\ \cdots \ A_N$

• $1\le N\le 100$
• $N\le M\le 10^5$
• $1\le A_i\le M$
• $A_i\neq A_j$ if $i\neq j$
• All inputs are integers

Output

Output the answer $\bmod{998244353}$.

Sample

2 3
1 2

5

1 11
11

2

3 141
5 9 2

113653783