We have a tree with $2^N-1$ vertices. The vertices are numbered $1$ through $2^N-1$. For each $1\leq i \lt 2^{N-1}$, 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 is given from Standard Input in the following format: >$N$ $D$ #### Constraints - $2 \leq N \leq 10^6$ - $1 \leq D \leq 2\times 10^6$ - All values in input are integers.

Print the answer.

***For Sample #1:*** The following figure describes the given tree.  There are $14$ pairs of vertices such that the distance between them is $2$: $(1,4),(1,5),(1,6),(1,7),(2,3),(3,2),(4,1),(4,5),(5,1),(5,4),(6,1),(6,7),(7,1),(7,6)$.

AtCoder [ABC220E]