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())
p = pow(10,9)+7
li = [1]*(n+2)

counter = 0
k = min(k,n-1)

for a in range(1,n+1):
    li[a] = a*li[a-1]%p

def comb(a,b):
    if b<1:
        return 1
    return li[a]*pow(li[b],p-2,p)*pow(li[a-b],p-2,p)


for i in range(k+1):
    counter += comb(n,i)*comb(n-1,i)%p
    #nCi*  (n-1)Cn-i-1


    #n人をn-iのぐるーぷに分ける

print(counter%p)