#FLWRS. Flowers

Flowers

Hanadi has N flower pots each with a unique flower. The pots are arranged along in a line.

One day, She decided to change their order under the condition that no two pots that were

originally next to each other remain next to each other.

 

Task

write a program that is given the number of pots, calculates the number of possible orders

satisfying the condition modulo a given integer M.

 

Constraints

1N2,000                         The number of pots.

2M1,000,000,000


Input

  • Line 1 contains the integer N, the number of flower pots.
  • Line 2 contains the integer M.

Output

A single line containing one integer between 0 and M-1 (inclusive): the number of possible

orders modulo M.

 

Example

Input:
5
11
Output:
3
For 5 pots, there are 14 orders satisfying Hanadi's condition, assuming the original order
of pots was "ABCDE"
Then the 14 possible orders are:

ACEBD

ADBEC

BDACE

BDAEC

BECAD

CADBE

CAEBD

CEADB

CEBDA

DACEB

DBEAC

DBECA

EBDAC

ECADB


14 modulo 11 = 3

So the answer is 3


 

  • Number of test-cases is 28.