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.

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.

Constraints

1 ≤ N ≤ 2,000

2 ≤ M ≤ 1,000,000,000

Number of test cases is 28.

Example

Input:
5
11

Output:
3

Explanation

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.