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).

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).

Constraints

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

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

• (0, 0, 3)
• (0, 1, 2)
• (0, 2, 1)
• (0, 3, 0)
• (1, 0, 2)
• (1, 1, 1)
• (1, 2, 0)
• (2, 0, 1)
• (2, 1, 0)
• (3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

见题面 Input 部分

见题面 Output 部分