Let the value of a connected undirected graph be the length of the shortest path from $1$ to $N$. Compute the sum of the values of all connected simple graphs with $N$ vertices and $M$ edges of length $1$ for each $M\in [N-1,R]$. Since the answers may be very large, output them modulo the prime $P$.

Constraints

$2\le N\le 60$

$N-1\le R\le \frac{N(N-1)}{2}$

${10}^8\le P\le {10}^9$

$P$ is prime.

Subtask 1 [30%]

$N,R\le 15$

Subtask 2 [20%]

$N,R\le 35$

Subtask 3 [30%]

$N\le 35$

Subtask 4 [20%]

No additional constraints.

Input Specification

The first and only line contains $3$ integers $N$, $R$, and $P$.

Output Specification

On a single line, output the desired values modulo $P$.

Sample Input 1

3 3 100000007

Sample Output 1

4 1

Explanation for Sample 1

There are three graphs with $3$ nodes and $2$ edges. One has a value of $2$, and two have a value of $1$. There is one graph with $3$ nodes and $3$ edges, and it has a value of $1$.

Sample Input 2

4 6 100000007

Sample Output 2

26 20 7 1