282. Isomorphism
Time limit per test: 1.25 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard
Let's call a
a non-oriented graph such that each pair of different vertices is connected by exactly one edge, colored in any of
M different colors. Two colored graphs are
if the vertices of the first graph can be renumbered in such a way that it becomes equal to the second graph (i.e. the colors of the edges are the same).
You are given
N,
M and a prime
P. Your task is to find the number of distinct non-isomorphic graphs having
N vertices. The number should be output modulo
P.
Input
The only line of the input contains three integers
N,
M,
P (1≤
N≤ 53, 1≤
M≤ 1000,
N9).
Output
Output the answer to the problem in the only line of the output.
Example(s)
sample input | sample output |
1 1 2
|
1
|
sample input | sample output |
3 2 97
|
4
|
sample input | sample output |
3 4 97
|
20
|
Novosibirsk SU Contest #2, by Novosibirsk Team #1
