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

1 ≤ N ≤ 2,000                         The number of pots.

2 ≤ M ≤ 1,000,000,000

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.