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())
#階乗
F = 200005
mod = 10**9+7
fact = [1]*F
inv = [1]*F
for i in range(2,F):
    fact[i]=(fact[i-1]*i)%mod
inv[F-1]=pow(fact[F-1],mod-2,mod)
for i in range(F-2,1,-1):
    inv[i] = (inv[i+1]*(i+1))%mod

ans=1
for i in range(1,min(n,k+1)):
    comb=(fact[n]*inv[i]*inv[n-i])%mod
    h=(fact[n-1]*inv[i]*inv[n-1-i])%mod
    ans=(ans+comb*h)%mod
print(ans)