Whiskerwood Junctions

Time limit: 3000 msMemory limit: 256 MB

Whiskerwood has $N$ clearings connected by trails. The trails form a tree, and the clearings are numbered $1,2,\ldots,N$ .

Exactly $K$ fish baskets are hidden at $K$ distinct clearings. Every set of $K$ clearings is chosen with equal probability.

After discovering the baskets, Gats forms the hunting network: the unique smallest connected subgraph of the tree containing every clearing with a basket. When $K=1$ , this network consists of one clearing and no trails.

A clearing is called a junction if it is incident to at least $3$ trails within the hunting network. Let $J$ be the number of junctions.

Find the expected value of $J$ , modulo $998244353$ .

Input

The first line contains two integers $N$ and $K$ ( $1 \le N \le 2 \times 10^5$ , ), the number of clearings and fish baskets.

Output

Let the exact expected number of junctions, in lowest terms, be $\frac{A}{B}$ . Let $P=998244353$ ; the constraints guarantee that $B \not\equiv 0 \pmod P$ .

Samples

Sample 1

Input

1 1

Output

The hunting network consists of the only clearing and has no junctions.

Sample 2

Input

Output

748683265

There are four equally likely basket placements. Only the placement using clearings $2$ , $3$ , and $4$ makes clearing $1$ a junction, so the expected value is $\frac{1}{4}$ .

Whiskerwood Junctions

Input

Output

Samples

Sample 1

Sample 2

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Submissions

Sample 3