Score : $1200$ points
$N$ 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 $M$.
Input is given from Standard Input in the following format:
$N$ $M$
Print the number of ways to assign scores to the problems, modulo $M$.
2 998244353
3
The possible assignments are $(1, 1)$, $(1, 2)$, $(2, 2)$.
3 998244353
7
The possible assignments are $(1, 1, 1)$, $(1, 2, 2)$, $(1, 3, 3)$, $(2, 2, 2)$, $(2, 2, 3)$, $(2, 3, 3)$, $(3, 3, 3)$.
6 966666661
66
96 925309799
83779