489. Extremal Permutations
Time limit per test: 0.5 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard
A member
ai of the sequence
a1,
a2, ·s,
an is called a
if either
ai >
ai-1 and
ai >
ai+1 (local maximum) or
ai <
ai-1 and
ai <
ai+1 (local minimum). A sequence
p1,
p2, ·s,
pn is called a
of the integers from 1 to
n if each of the integers appears in the sequence exactly once. A permutation is called
if each member (except the first and the last) is a local extreme.
Compute the total number of extremal permutations of the integers from 1 to
n and output the result modulo
m.
Input
The first and only line of the input file contains the integers
n (
) and
m (1 ≤
m ≤ 10
9).
Output
The output file should contain a single integer, the remainder from division of the total number of extremal permutations of integers from 1 to n by the given integer
m.
Example(s)
sample input | sample output |
3 10
|
4
|
sample input | sample output |
3 3
|
1
|
Note. The extremal permutations of 1·s3 are (1, 3, 2), (2, 1, 3), (2, 3, 1) and (3, 1, 2).