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
M=10**9+7
n,k=map(int,input().split())
from functools import lru_cache
@lru_cache(None)
def f(x):
  if x: return x*f(x-1)%M
  return 1
l=[f(i) for i in range(n+1)]
a=0
for i in range(min(n,k+1)):
  c=l[n]*l[n-1]%M
  p=l[i]**2*l[n-i]*l[n-i-1]%M
  a+=c*pow(p,M-2,M)
print(a%M)