There are $N$ people called Person $1$, Person $2$, $\dots$, Person $N$, lined up in a row in the order of $(1,2,\dots,N)$ from the front. Person $i$ is wearing Color $c_i$.  
Takahashi repeated the following operation $K$ times: choose two People $i$ and $j$ arbitrarily and swap the positions of Person $i$ and Person $j$.  
After the $K$ operations have ended, the color that the $i$-th person from the front is wearing coincided with $c_i$, for every integer $i$ such that $1 \leq i \leq N$.  
How many possible permutations of people after the $K$ operations are there? Find the count modulo $998244353$.

Input is given from Standard Input in the following format:

```
$N$ $K$
$c_1$ $c_2$ $\dots$ $c_N$
```

Print the answer.

-   $2 \leq N \leq 200000$
-   $1 \leq K \leq 10^9$
-   $1 \leq c_i \leq N$
-   All values in input are integers.

3

1

Here is an example of a possible sequence of Takahashi's operations.

• In the 1-st operation, he swaps the positions of Person 1 and Person 3, resulting in a permutation (3,2,1).
  In the 2-nd operation, he swaps the positions of Person 2 and Person 3, resulting in a permutation (2,3,1).
  In the 3-rd operation, he swaps the positions of Person 1 and Person 3, resulting in a permutation (2,1,3).

Note that, during the sequence of operations, the color that the i-th person from the front is wearing does not necessarily coincide with $c_i$.