Strange Function

2000ms

524288K

Description:

Let's define the function $$$f$$$ of multiset $$$a$$$ as the multiset of number of occurences of every number, that is present in $$$a$$$.

E.g., $$$f(\{5, 5, 1, 2, 5, 2, 3, 3, 9, 5\}) = \{1, 1, 2, 2, 4\}$$$.

Let's define $$$f^k(a)$$$, as applying $$$f$$$ to array $$$a$$$ $$$k$$$ times: $$$f^k(a) = f(f^{k-1}(a)), f^0(a) = a$$$.

E.g., $$$f^2(\{5, 5, 1, 2, 5, 2, 3, 3, 9, 5\}) = \{1, 2, 2\}$$$.

You are given integers $$$n, k$$$ and you are asked how many different values the function $$$f^k(a)$$$ can have, where $$$a$$$ is arbitrary non-empty array with numbers of size no more than $$$n$$$. Print the answer modulo $$$998\,244\,353$$$.

Input:

The first and only line of input consists of two integers $$$n, k$$$ ($$$1 \le n, k \le 2020$$$).

Output:

Print one number — the number of different values of function $$$f^k(a)$$$ on all possible non-empty arrays with no more than $$$n$$$ elements modulo $$$998\,244\,353$$$.

Sample Input:

3 1

Sample Output:

Sample Input:

5 6

Sample Output:

Sample Input:

10 1

Sample Output:

Sample Input:

10 2

Sample Output:

Informação

Provedor Codeforces

Código CF1310E