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())
mod=10**9+7
bikkuri=[0 for i in range(2*n+5)]
bikkuri[0]=1
gyaku=[0 for i in range(2*n+5)]
gyaku[0]=1
for i in range(1,2*n+5):
    bikkuri[i] = (i * bikkuri[i-1])%mod
    gyaku[i]=pow(bikkuri[i], mod-2, mod)
def comb(a,b):
    return bikkuri[a]*gyaku[b]%mod*gyaku[a-b]%mod
if n<=k:
    ans=comb(2*n-1,n)%mod
elif k==1:
    ans=n*n-1
    ans%=mod
else:
    ans=0
    for i in range(k+1):
        if i==0:
            ans+=1
            ans%=mod
        else:
            ans+=comb(n,n-i)*comb(n-1,i)
            ans%=mod
print(ans)
    