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