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 nCr_frL(n,r,mod):
    ret=[1,n%mod]
    for i in range(2,r+1):
        inv=pow(i,mod-2,mod)
        ret.append((ret[-1]*(n-i+1)*inv)%mod)
    return ret

N,K=map(int,input().split())
MOD=10**9+7
com1=nCr_frL(N,N,MOD) # nCi
com2=nCr_frL(N-1,N-1,MOD) # n-1Ci

if K>N-1:
    K=N-1
ans=0
for m in range(K+1):
    ans+=(com1[m]*com2[N-m-1])%MOD
print(ans%MOD)

