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.

Input

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

Output

Print the answer.

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.

Sample Input 1

3 1 282282277

Sample Output 1

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.

Sample Input 2

50 25 998244353

Sample Output 2

131276976

Print the number modulo P.

见题面 Input 部分

见题面 Output 部分