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 =list(map(int,input().split()))

mod = 10**9+7
ans = 1%mod
left_combination = 1
right_combination = 1

for i in range(1,min(k,n-1)+1):
    left_combination = (left_combination*(n+1-i)*pow(i,mod-2,mod))%mod
    right_combination = (right_combination*(n-i)*pow(i,mod-2,mod))%mod
    ans = (ans + (left_combination*right_combination)%mod)%mod

print(ans)