Problem Statement

You are given positive integers $N$ and $K$. Consider an undirected tree $T$ with $(2K + 1)N + 1$ vertices labeled from $1$ to $(2K + 1)N + 1$. Among all such trees, find the number, modulo $998244353$, of trees that satisfy the following condition.

• It is possible to remove all edges from $T$ by repeating the following operation:
• Choose a path of length $2K + 1$ and remove all edges in it. Formally, choose a sequence of distinct vertices $v_0, v_1, \dots, v_{2K+1}$ such that there exists an edge $(v_i, v_{i+1})$ for all $i$ such that $0 \leq i \leq 2K$, and remove the edge $(v_i, v_{i+1})$ for all $i$ such that $0 \leq i \leq 2K$.

Constraints

• $1 \leq N \leq 1.3 \times 10^5$
• $1 \leq K \leq 50$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N K

Output

Print the number, modulo $998244353$, of trees with $(2K + 1)N + 1$ vertices satisfying the condition.