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())

# Function of Combination mod M
# set n >= max p expected
M = 10**9+7


if k >= n-1:
    fac = [1]+[0]*(2*n-1)
    for i in range(1,2*n): fac[i] = fac[i-1]*i %M
    comb = lambda p,q:(fac[p]*pow(fac[q],M-2,M)*pow(fac[p-q],M-2,M))%M
    y = comb(2*n-1,n-1)
    
else:
    y = 1
    c1,c2=1,1
    for i in range(1,k+1):
        p = pow(i,M-2,M)
        c1 = c1*(n+1-i)*p%M
        c2 = c2*(n-i)*p%M
        y += c1*c2%M
        # y = (y+c1*c2)%M
print(y%M)
