Cat Councils at the Crossroads

Time limit: 2000 msMemory limit: 256 MB

A group of cats visits a tree with $N$ vertices. A set of exactly $K$ distinct vertices is chosen uniformly at random from all $\binom{N}{K}$ possible sets, and one cat is placed at each chosen vertex.

Consider a vertex $v$ . Temporarily remove $v$ and every edge incident to it. Each resulting connected component represents one direction from $v$ . A direction is called active if its component contains at least one cat.

A cat placed directly at $v$ does not make any direction active. A council forms at $v$ if at least $3$ of its directions are active.

Let $X$ be the total number of vertices at which a council forms. Find the expected value of $X$ , modulo $10^9+7$ .

Input

The first line contains two integers $N$ and $K$ ( $3 \le N \le 2\cdot 10^5$ , ), the number of vertices and the number of chosen vertices.

Output

Let $E$ be the expected number of vertices at which a council forms. Write $E=\frac{p}{q}$ , where $p$ and are integers and .

Samples

Sample 1

Input

Output

250000002

There are $4$ equally likely chosen sets. A council forms only when the chosen set is $\{2,3,4\}$ , so the expectation is $\frac{1}{4}$ . Its required modular representation is .

Cat Councils at the Crossroads

Input

Output

Samples

Sample 1

Submit

Submissions

Sample 2