Whisker Junction Festival

Time limit: 2000 msMemory limit: 256 MB

A festival is held on a tree with $N$ vertices. Vertex $i$ has a cat whose signal bell has volume $A_i$ .

Exactly $K$ distinct vertices are selected uniformly at random from all $\binom{N}{K}$ possible sets, and a fish is placed at every selected vertex.

Consider the cat at a vertex $v$ . Temporarily remove $v$ and all edges incident to it. This separates the remaining vertices into one or more connected components. The cat at $v$ rings its bell if at least two different components each contain at least one selected vertex.

If $v$ itself is selected, its fish belongs to none of the components and does not by itself help the cat ring.

The total signal is the sum of $A_v$ over all cats whose bells ring. Find the expected total signal modulo $10^9+7$ .

Input

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

Output

Let the expected total signal be the rational number $x/y$ in lowest terms. Print

x\cdot y^{-1}\bmod (10^9+7),

Samples

Sample 1

Input

Output

333333336

Only the cat at vertex $2$ can ring. It rings when vertices $1$ and $3$ are selected, so the expected total signal is $1/3$ , represented modulo $10^9+7$ .

Whisker Junction Festival

Input

Output

Samples

Sample 1

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Submissions

Sample 2