Problem Statement

For a permutation $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$, define integers $L(P)$ and $R(P)$ as follows:

• Consider $N$ buildings arranged in a row from left to right, with the height of the $i$-th building from the left being $P_i$. Then $L(P)$ is the number of buildings visible when viewed from the left, and $R(P)$ is the number of buildings visible when viewed from the right. More formally, $L(P)$ is the count of indices $i$ such that $P_j < P_i$ for all $j < i$, and $R(P)$ is the count of indices $i$ such that $P_i > P_j$ for all $j > i$.

You are given integers $N$ and $K$. Find, modulo $998244353$, the count of all permutations $P$ of $(1,2,\dots,N)$ such that $L(P)-R(P)=K$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $|K| \leq N-1$
• All input values are integers.

Input

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

N K

Output

Print the answer.