Problem Scores

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.

Examples

Input

2 998244353

Output

3

Input

3 998244353

Output

7

Input

6 966666661

Output

66

Input

96 925309799

Output

83779

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N M

outputFormat

Output

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

Examples

Input

2 998244353

Output

3

Input

3 998244353

Output

7

Input

6 966666661

Output

66

Input

96 925309799

Output

83779

样例

3 998244353

7