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
f=[1]
for i in range(10**6):f+=[f[-1]*(i+1)%mod]
def comb(a,b):return f[a]*pow(f[b],mod-2,mod)*pow(f[a-b],mod-2,mod)%mod

n,k=map(int,input().split())
ans=comb(n*2-1,n-1)
if k>=n-1:print(ans);exit()
for i in range(n-1,k,-1):
  #ansからi回の操作では不可能な組み合わせを引く
  #0*i + any*(n-i)
  #つまり((n-i)個の部屋にn人が入る組み合わせ)*nC(n-i)
  #各部屋には必ず1人は入る
  #つまり(n-1)Ci
  anss=comb(n-1,i)*comb(n,n-i)%mod
  ans=ans+(mod-anss)
  ans%=mod
print(ans)