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
f=[1]*(2*n+1)
for i in range(2,2*n+1):
    f[i]=f[i-1]*i%Mod
def f_inverse(i):
    return pow(f[i],Mod-2,Mod)
f_inv=[f_inverse(i) for i in range(2*n+1)]
def comb(n,i):
    return f[n]*f_inv[i]*f_inv[n-i]%Mod

Ans=0
for x in range(0,min(k+1,n)):
    Ans=(Ans+comb(n,x)*comb(n-1,x))%Mod
print(Ans)