Problem Statement

You are given an odd number N and a non-negative integer K.
Find the number, modulo 998244353, of sequences of integer pairs $((L_1,R_1),(L_2,R_2),\dots,(L_N,R_N))$ satisfying all of the following conditions.

• $(L_1,R_1,L_2,R_2,\dots,L_N,R_N)$ is a permutation of the integers from 1 to 2N.
• $L_1 \leq L_2 \leq \dots \leq L_N$.
• $L_i \leq R_i$ \ $(1 \leq i \leq N)$.
• There are exactly K indices i\ $(1\leq i \leq N)$ such that L_i+1=R_i.
• There is a rooted binary tree T with N vertices numbered from 1 to N such that the following holds:
• vertices i and j have an ancestor-descendant relationship in $T \iff intervals [L_i,R_i]$ and [L_j,R_j] intersect.

Here, a rooted binary tree is a rooted tree where each vertex has 0 or 2 children. Vertices i and j are said to have an ancestor-descendant relationship in a tree T if either vertex j exists on the simple path connecting the root to vertex i, or vice versa.

Input

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

Output

Print the answer.

Constraints

• $1 \leq N < 2 \times 10^5$
• $0 \leq K \leq N$
• N is odd.
• All input values are integers.

Sample Input 1

3 1

Sample Output 1

2

For example, if (L_1,R_1)=(1,5),(L_2,R_2)=(2,3),(L_3,R_3)=(4,6), then i=2 is the only pair with L_i+1=R_i. Also, the fifth condition is satisfied by a tree where vertex 1 is the root, and its children are vertices 2 and 3.

Sample Input 2

1 0

Sample Output 2

0

Sample Input 3

521 400

Sample Output 3

0

Sample Input 4

199999 2023

Sample Output 4

283903125

见题面 Input 部分

见题面 Output 部分