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())

def calc(n,m):
    y = [1]*(n+1)
    for i in range(n):
        y[i+1] = (y[i]*(i+1))%m
        
    return y

def calc2(n,a,m,y):
    x = (y[a]*y[n-a])%m
    return (y[n]*pow(x, m-2, m))%m

m = 10**9+7
y = calc(2*n-1,m)
if k >= n-1:
    print(calc2(2*n-1, n-1, m, y))
else:
    s = 0
    for i in range(n-k-1):
        s += calc2(n-1,i,m,y)*calc2(n,i+1,m,y)
    print((calc2(2*n-1, n-1, m, y)-s)%m)