Black Soul Gem

F: Red-Black Soul Gem

problem

Homu-chan has the mysterious power to change the soul game to red or black, and to connect two different soul games with a magic thread. By using this power, Homu-chan can create a magic square by Sorujemu.

Homu-chan was wondering how many different magic squares there were when there were N numbered magic squares numbered from 1 to N, and the following conditions were met:

• You can only connect once between any of the two sources.
• All the colors of the game are either red or black.
• For any game, it is connected to at least one of the games whose color is different from its own.

At this time, the magic square can be regarded as a graph with the sorujemu as the apex and the magic thread as the side. Note that the graph does not have to be concatenated.

Homu-chan is not good at calculating, so let's create a fast program instead and calculate the number of different magic squares. However, the number is expected to be very large, so we will find the remainder after dividing by a prime number M.

Note that the magic squares G and H are different because the colors of G and H are different for a certain magic square v, or the pair u and v of a certain magic square is one of G and H. It means that it is connected only with.

Input format

N M

Constraint

• 2 \ leq N \ leq 2,000
• 10 ^ 8 \ leq M \ leq 10 ^ 9 + 7
• M is guaranteed to be prime

Output format

Divide the number of graphs that satisfy the condition by M and output the remainder as an integer on one line.

Input example 1

3 310779401

Output example 1

12

For example, the following magic squares meet the conditions.

Input example 2

7 566666561

Output example 2

98638848

For example, the following magic squares meet the conditions.

Input example 3

1010 1000000007

Output example 3

862232855

Note that we output the remainder after dividing by M.

Example

Input

3 310779401

Output

12

inputFormat

Input format

N M

Constraint

• 2 \ leq N \ leq 2,000
• 10 ^ 8 \ leq M \ leq 10 ^ 9 + 7
• M is guaranteed to be prime

outputFormat

Output format

Divide the number of graphs that satisfy the condition by M and output the remainder as an integer on one line.

Input example 1

3 310779401

Output example 1

12

For example, the following magic squares meet the conditions.

Input example 2

7 566666561

Output example 2

98638848

For example, the following magic squares meet the conditions.

Input example 3

1010 1000000007

Output example 3

862232855

Note that we output the remainder after dividing by M.

Example

Input

3 310779401

Output

12

样例

3 310779401

12