题目描述
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).
Examples
Input
3 2
Output
10
Input
200000 1000000000
Output
607923868
Input
15 6
Output
22583772
输入格式
见题面
输出格式
见题面