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():
    n,k=map(int,input().split())
    MOD=10**9+7

    def pre(n,MOD):
        a=1
        for i in range(1,n+1):
            a=(a*i)%MOD
        an=a
        b=pow(a,MOD-2,MOD)
        bs=[1]*(n+1)
        bs[n]=b
        for i in range(n,1,-1):
            b=b*i%MOD
            bs[i-1]=b
        return an,bs

    a,b=pre(n-1,MOD)
    ans=1
    for i in range(1,min(n-1,k)+1):
        s=(a*n*b[i])%MOD
        s=(s*b[n-i])%MOD
        s=(s*a*b[n-i-1])%MOD
        s=(s*b[i])%MOD
        ans+=s
        ans%=MOD
    print(ans)
    
if __name__ == '__main__':
    main()