Below, a permutation of $(1,2,\ldots,N)$ is simply called a permutation.

For two permutations $A=(A_1,A_2,\ldots,A_N),B=(B_1,B_2,\ldots,B_N)$, let us define their similarity as the number of integers $i$ between $1$ and $N-1$ such that:

-   $(A_{i+1}-A_i)(B_{i+1}-B_i)>0$.

Find the number, modulo a prime number $P$, of pairs of permutations $(A,B)$ whose similarity is $K$.

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

```
$N$ $K$ $P$
```

Print the answer.

-   $2\leq N \leq 100$
-   $0\leq K \leq N-1$
-   $10^8 \leq P \leq 10^9$
-   $P$ is a prime number.
-   All values in the input are integers.

16

For instance, below is a pair of permutations that satisfies the condition.

• A=(1,2,3)
• B=(1,3,2)

Here, we have $(A_2−A_1)(B_2−B_1)>0$ and $(A_3−A_2)(B_3−B_2)<0$, so the similarity of A and B is 1.