Problem Statement

Given are integers N and K, and a prime number P. Find the number, modulo P, of directed graphs G with N vertices that satisfy below. Here, the vertices are distinguishable from each other.

• G is a tournament, that is, G contains no duplicated edges or self-loops, and exactly one of the edges $u\to$ v and $v\to$ u exists for any two vertices u and v.
• The in-degree of every vertex in G is at most K.
• For any four distinct vertices a, b, c, and d in G, it is not the case that all of the six edges $a\to$ $b, b\to$ $c, c\to$ $a, a\to$ $d, b\to$ d, and $c\to$ d exist simultaneously.

Input

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

Output

Print the number of directed graphs that satisfy the conditions, modulo P.

Constraints

• $4 \leq N \leq 200$
• $\frac{N-1}{2} \leq K \leq N-1$
• 10^8<P<10^9
• N and K are integers.
• P is a prime number.

Sample Input 1

4 3 998244353

Sample Output 1

56

Among the 64 graphs with four vertices, 8 are isomorphic to the forbidden induced subgraphs, and the other 56 satisfy the conditions.

Sample Input 2

7 3 998244353

Sample Output 2

720

Sample Input 3

50 37 998244353

Sample Output 3

495799508

见题面 Input 部分

见题面 Output 部分