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.

Sample Input 1Copy

2 998244353

Sample Output 1Copy

3

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

Sample Input 2Copy

3 998244353

Sample Output 2Copy

7

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 3Copy

6 966666661

Sample Output 3Copy

66

Sample Input 4Copy

96 925309799

Sample Output 4Copy

83779