Score : 1200 points

Problem Statement

N problems have been chosen by the judges, now it's time to assign scores to them!

Problem i must get an integer score A_i between 1 and N, inclusive. The problems have already been sorted by difficulty: A_1 \le A_2 \le \ldots \le A_N must hold. Different problems can have the same score, though.

Being an ICPC fan, you want contestants who solve more problems to be ranked higher. That's why, for any k (1 \le k \le N-1), you want the sum of scores of any k problems to be strictly less than the sum of scores of any k+1 problems.

How many ways to assign scores do you have? Find this number modulo the given prime M.

Constraints

2 \leq N \leq 5000
9 \times 10^8 < M < 10^9
M is a prime.
All input values are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of ways to assign scores to the problems, modulo M.

Sample Input 1

2 998244353

Sample Output 1

The possible assignments are (1, 1), (1, 2), (2, 2).

Sample Input 2

3 998244353

Sample Output 2

The possible assignments are (1, 1, 1), (1, 2, 2), (1, 3, 3), (2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3).

Sample Input 3

6 966666661

Sample Output 3

Sample Input 4

96 925309799