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
def combinations(n,k,mod):
    x,y = 1,1
    for i in range(k):
        x = (x*(n-i))%mod
        y = (y*(i+1))%mod
    return (x*pow(y,mod-2,mod))%mod
    

mod = 10**9+7
n,k = map(int,input().split())

def cmap(n,k):
    x = [1]
    y = [1]
    c = [1]
    for i in range(k+1):
        x.append((x[i]*(n-i))%mod)
        y.append((y[i]*(i+1))%mod)
        c.append((x[i+1]*pow(y[i+1],mod-2,mod))%mod)
    return c
    
#print(cmap(n,n))
nc=cmap(n,n-1)
n1c=cmap(n-1,n-2)

ans = 0
for i in range(min(n-1,k)+1):
    ans = (ans+(nc[i]*n1c[i]))%mod

print(ans)