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
n,k=map(int,input().split())
fact=[1]
for i in range(1,2*n):
  fact.append((fact[i-1]*(i+1))%(10**9+7))
factinv=[]
for i in range(n):
  factinv.append(pow(fact[i],10**9+5,10**9+7))
if k==1:
  print((n*(n-1))%(10**9+7))
elif k>=n-1:
  print((fact[2*n-2]*factinv[n-1]*factinv[n-2])%(10**9+7))
else:
  ans=1
  for i in range (k):
    ans=(ans+fact[n-1]*factinv[i]*factinv[n-i-2]*fact[n-2]*factinv[i]*factinv[n-i-3])%(10**9+7)
  print(ans)