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
def main():
    mod=1000000007
    n,k=map(int,input().split())
    m=2*n
    Fact=[1] #階乗
    for i in range(1,m+1):
        Fact.append(Fact[i-1]*i%mod)
    Finv=[0]*(m+1) #階乗の逆元
    Finv[-1]=pow(Fact[-1],mod-2,mod)
    for i in range(m-1,-1,-1):
        Finv[i]=Finv[i+1]*(i+1)%mod
    def comb(n,r):
        if n<r:
            return 0
        return Fact[n]*Finv[r]*Finv[n-r]%mod
    
    if k>=n-1:
        return comb(2*n-1,n-1)
    ans=1
    for i in range(1,k+1):
        ans+=comb(n,i)*comb(n-1,n-i-1)
        ans%=mod
    return ans
    
if __name__=='__main__':
    print(main())