p02769 AtCoder Beginner Contest 156 - Roaming
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
```python
n,k=map(int,input().split())
mod=10**9+7
lim=n
fcl=[1]*(lim+1)
for i in range(1,lim+1):
  fcl[i]=(fcl[i-1]*i)%mod
def comb(x,y,p):
  return ((fcl[x]*pow(fcl[y],p-2,p))%p*pow(fcl[x-y],p-2,p))%p
ans=0
for i in range(min(n,k+1)):
  ans+=comb(n-1,n-i-1,mod)*comb(n,i,mod)
  ans%=mod
print(ans)
```