Problem Statement

There is a building with $n$ rooms, numbered $1$ to $n$.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room $i$ goes to another room $j~ (i \neq j)$.

Initially, there was one person in each room in the building.

After that, we know that there were exactly $k$ moves happened up to now.

We are interested in the number of people in each of the $n$ rooms now. How many combinations of numbers of people in the $n$ rooms are possible?

Find the count modulo $(10^9 + 7)$.

Constraints

• All values in input are integers.
• $3 \leq n \leq 2 \times 10^5$
• $2 \leq k \leq 10^9$

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of possible combinations of numbers of people in the $n$ rooms now, modulo $(10^9 + 7)$.