Problem Statement

Solve the following problem for $T$ cases.

Find the number, modulo $998244353$, of ways to place $N$ people on a number line such that the following conditions are satisfied.

• The coordinate of every person is an integer between $1$ and $M$, inclusive.
• For every $i\ (1 \le i \le N)$, let $l$ be the number of people at coordinates smaller than that of person $i$, and let $r$ be the number of people at coordinates larger than that of person $i$; then $\max(l,r)=A_i$.

Here, $2$ placements are considered different if and only if there exists a person $i$ such that the coordinate of person $i$ differs between them.

Input

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

Each case is given in the following format.

$N$ $M$
$A_1$ $A_2$ $\ldots$ $A_N$

• $1 \le T \le 2 \times 10^5$
• $1 \le N,M \le 2 \times 10^5$
• $0 \le A_i \le N-1$
• The sum of $N$ over all cases does not exceed $2\times 10^5$.
• All input values are integers.

Output

Print $T$ lines. On the $i$-th line, print the answer for $\text{case}_i$.

Sample

3
5 5
4 3 2 3 4
1 5
0
7 7
1 1 1 1 6 1 1

4
5
42