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 i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
mod=10**9+7
def bp(a,n):
        r=1
        while(n):
           if n%2:
              r=r*a%mod
           a=a*a%mod
           n>>=1
        return r
[n,k]=i2()
if n<=k:
   x=1
   for i in range(n-1):
      x*=2*n-1-i
      x%=mod
   y=1
   for i in range(n-1):
      y*=i+1
      y%=mod
   print((x*bp(y,10**9+5))%mod)   
   
else:
   x=1
   y=1
   t=1
   for i in range(k):
      t*=i+1
      t%=mod
      y*=n-1-i
      y%=mod
      y*=n-i
      y%=mod
      c=bp(t,10**9+5)
      x+=y*c*c
      x%=mod
   print(x)   