The Two-Bank Lantern Raffle

Time limit: 2000 msMemory limit: 256 MB

The kingdom of cats has $N$ stations connected by $N-1$ two-way rope bridges. It is possible to travel between every pair of stations.

At the start of the Lantern Festival, exactly $K$ stations are selected uniformly at random among all $\binom{N}{K}$ subsets of that size. One traveler cat is placed at each selected station.

Every bridge has two bridgekeeper cats, one on each bank. The bridgekeepers are fixed and are not traveler cats. For each bridge, the following raffle is performed:

Removing the bridge separates the stations into two components, one belonging to each bank.
On each bank, its bridgekeeper makes a list containing their own name and the name of every traveler cat whose station lies in that bank's component.
Each bank independently draws one name uniformly at random from its list.
The bridge's lantern is lit if both banks draw the name of their own bridgekeeper.

All bank draws are independent after the traveler stations have been selected.

Find the expected total number of lit bridge lanterns.

Input

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

Output

Let $E$ be the expected number of lit lanterns. Write $E$ as a reduced fraction $p/q$ , where $q>0$ and $\gcd(p,q)=1$ .

Samples

Sample 1

Input

3 2
1 2
2 3

Output

221832079

For this path with $K=2$ , the expected number of lit lanterns is $5/9$ . Its required modular representation is $221832079$ .

Sample 2

Input

Output

124780545

For this star, the expected total number of lit lanterns is $7/8$ , which has the shown modular representation.

Sample 3

Input

1 0

Output