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
mod=10**9+7
n,k=map(int,input().split())
ans=1
coef1=n
coef2=n-1
for i in range(1,min(k+1,n)):
  tmp=1
  tmp*=coef1
  tmp%=mod
  tmp*=coef2
  tmp%=mod
  ans+=tmp
  ans%=mod  
  coef1*=n-i
  coef1%=mod
  coef1*=pow(i+1,mod-2,mod)
  coef1%=mod
  coef2*=n-1-i
  coef2%=mod
  coef2*=pow(i+1,mod-2,mod)
  coef2%=mod
print(ans)