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
def comb(n,m,p=10**9+7):
    buf=perm[n]*inv[m]
    buf%=MOD
    buf*=inv[n-m]
    buf%=MOD
    return buf
def inv_mod(a):
  return pow(a,MOD-2,MOD)

perm=[1]*(2*n+1)
for i in range(1,2*n+1):
    perm[i]=perm[i-1]*(i)
    perm[i]%=MOD
inv=[1]*(2*n+1)
inv[-1]=inv_mod(perm[-1])
for i in range(2*n-1,-1,-1):
    inv[i]=inv[i+1]*(i+1)
    inv[i]%=MOD
#print(comb(5,2))
buf=comb(2*n-1,n)
for j in range(k+1,n):
    x=comb(n,j)*comb(n-1,j)
    x%=MOD
    buf-=x
    buf%=MOD
print(buf)