I. Imprisoned XII
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Given two integers $$$N$$$ and $$$K$$$, count the number of pairs of non-decreasing sequences $$$(a, b)$$$, each of length $$$N$$$, that satisfy:

  • $$$a_1 = b_1 = 0$$$
  • $$$\forall 2 \leq i \leq N, a_i - a_{i - 1} \leq 1$$$
  • $$$\forall 2 \leq i \leq N, b_i - b_{i - 1} \leq 1$$$
  • $$$\forall 1 \leq i \leq N, a_i - b_i \leq K$$$

Since the number may be huge, output the result modulo $$$998244353$$$.

Input

The input only contains one line with two integers $$$N$$$, $$$K$$$.

  • $$$1 \leq N \leq 10^6$$$
  • $$$0 \leq K \leq N$$$
Output

Output a single line with one integer — the number of pairs of non-decreasing sequences $$$(a, b)$$$ that satisfy the conditions, modulo $$$998244353$$$.

Examples
Input
4 1
Output
56
Input
8 3
Output
15808
Input
56562 48763
Output
444024476