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
MOD = 1000000007#い　つ　も　の
n,k = map(int,input().split())

nCk = 1#nC0
ans = 1

if k > n-1:
    k = n-1

for i in range(1,k+1,1):
    nCk = (((nCk*(n-i+1))%MOD)*pow(i,1000000005,1000000007))%MOD
    ans = (ans%MOD + ((((nCk*nCk)%MOD)*(n-i)%MOD)*pow(n,1000000005,1000000007)%MOD)%MOD)%MOD

print(ans)
