Problem Statement

We have a tree with 2^N-1 vertices.
The vertices are numbered 1 through 2^N-1. For each $1\leq i < 2^{N-1}$, the following edges exist:

• an undirected edge connecting Vertex i and Vertex 2i,
• an undirected edge connecting Vertex i and Vertex 2i+1.

There is no other edge.
Let the distance between two vertices be the number of edges in the simple path connecting those two vertices.
Find the number, modulo 998244353, of pairs of vertices (i, j) such that the distance between them is D.

Input

Input is given from Standard Input in the following format:
N D

Output

Print the answer.

Constraints

• $2 \leq N \leq 10^6$
• $1 \leq D \leq 2\times 10^6$
• All values in input are integers.

Sample Input 1

3 2

Sample Output 1

14

The following figure describes the given tree.

There are 14 pairs of vertices such that the distance between them is 2: (1,4),(1,5),(1,6),(1,7),(2,3),(3,2),(4,1),(4,5),(5,1),(5,4),(6,1),(6,7),(7,1),(7,6).

Sample Input 2

14142 17320

Sample Output 2

11284501

见题面 Input 部分

见题面 Output 部分