Presenters

The workshop needs a presenting sequence. There are $n$ distinct people, and you must choose exactly $k$ of them to present. Order matters: the person in slot $1$ speaks first, the person in slot $2$ speaks second, and so on. The same set of $k$ people in a different speaking order counts as a different sequence.

Count the number of possible presenting sequences. Since the answer can be large, output it modulo $10^9 + 7$.

Input

A single line containing two integers $n$ and $k$.

Output

Print one integer: the number of presenting sequences of length $k$, modulo $10^9 + 7$.

Constraints

• $0 \le n, k \le 10^6$

Example 1

5 2

20

Explanation

There are $5$ choices for slot $1$ and then $4$ remaining choices for slot $2$, so there are $5 \times 4 = 20$ ordered sequences. Alice then Bob is different from Bob then Alice.

Example 2

4 0

1

Explanation

There is exactly one empty presenting sequence.

Example 3

3 5

0

Explanation

You cannot fill $5$ slots using only $3$ people.