P6189 [NOI Online #1 Junior] Running

Little H is a child who loves sports. One day, he wants to make a running plan for himself. Little H plans to run $n$ meters in total. In the $i$-th minute ($i \geq 1$), he will run $x_i$ meters ($x_i$ is a positive integer), but the total duration is not fixed. As the running time increases, Little H will get more and more tired, so his plan must satisfy that for any $i$ ($i > 1$), $x_i \leq x_{i-1}$. Now Little H wants to know how many different plans satisfy the conditions. Two plans are different if and only if the total duration is different, or there exists an $i$ such that $x_i$ is different in the two plans. Since the final answer may be very large, you only need to output the result modulo $p$.

The input contains only one line with two integers, representing the total meters $n$ and the modulus $p$.

Output one line with one integer, representing the answer modulo $p$.

#### Explanation of Sample Input/Output 1 The five different plans are: $\{1,1,1,1\}$, $\{2,1,1\}$, $\{3,1\}$, $\{2,2\}$, $\{4\}$. --- #### Constraints This problem has $10$ test points. The information for each test point is shown in the table below. | Test Point ID | $n \leq$ | Test Point ID | $n \leq$ | | :----------: | :---------: | :----------: | :---------: | | $1$ | $5$ | $6$ | $2\times 10^3$ | | $2$ | $10$ | $7$ | $5\times 10^3$ | | $3$ | $50$ | $8$ | $2\times 10^4$ | | $4$ | $100$ | $9$ | $5\times 10^4$ | | $5$ | $500$ | $10$ | $10^5$ | For all test points, it is guaranteed that $1 \leq n \leq 10^5$, $1 \leq p < 2^{30}$. Translated by ChatGPT 5