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
"""
E
"""
mod=10**9+7
MAX=4*10**5+100

g1=[1,1]
for i in range(2,MAX+1):
    num_1=g1[-1]*i%mod
    g1.append(num_1)
    
def cmb(n,r):
    return g1[n]*pow(g1[r],mod-2,mod)*pow(g1[n-r],mod-2,mod)%mod


N,K=map(int,input().split())

ans=cmb(2*N-1,N)


if K>=N:
    print(ans)
    
else:
    num=cmb(N,N-K-1)
    S=0
    for i in range(N-K-1,0,-1):
        S=(S+cmb(N-1,i-1)*cmb(N,i))%mod
        
    ans=(ans-S)%mod
    print(ans)