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())
mod=10**9+7
def cmb(n,r,mod):
  return A[n]*B[n-r]*B[r]%mod
A=[1,1]
B=[1,1]
for i in range(n):
  A.append(A[-1]*(i+2)%mod)
  B.append(B[-1]*pow((i+2),mod-2,mod)%mod)
if k<n:
  ans=0
  for i in range(k+1):
    ans=(ans+cmb(n,i,mod)*cmb((n-1),i,mod))%mod
  print(ans)
else:
  ans=0
  for i in range(n):
    ans=(ans+cmb(n,i,mod)*cmb((n-1),i,mod))%mod
  print(ans)