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

N=n*2
fac=[1]*(N+1)
for i in range(1,N+1):
    fac[i]=fac[i-1]*i%MOD
ifac=[pow(fac[N],MOD-2,MOD)]*(N+1)
for i in range(N,0,-1):
    ifac[i-1]=ifac[i]*i%MOD

ans=0
if k>=n-1:
    ans=fac[n+n-1]*ifac[n]*ifac[n-1]%MOD
else:
    for i in range(k+1):
        if i>n: break
        tmp=fac[n]*ifac[n-i]*ifac[i]%MOD
        tmp=tmp*fac[i+n-i-1]*ifac[n-i-1]*ifac[i]%MOD
        ans=(ans+tmp)%MOD

print(ans)