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
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x
    if m%2==0:
        return (pow(x,m//2)**2)%p
    else:
        return (x*(pow(x,(m-1)//2)**2)%p)%p
    
n,k = map(int,input().split())
A = [1 for _ in range(n+1)]
for i in range(2,n+1):
    A[i] = (i*A[i-1])%p
B = [1 for _ in range(n+1)]
B[n] = pow(A[n],p-2)
for i in range(n-1,1,-1):
    B[i] = (B[i+1]*(i+1))%p

cnt = 0
for i in range(min(k,n-1)+1):
    a = (A[n]*B[n-i]*B[i])%p
    b = (A[n-1]*B[n-1-i]*B[i])%p
    cnt = (cnt+a*b)%p
print(cnt)