Problem Statement

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 $K$.

Constraints

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

Input

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

N K P

Output

Print the answer.