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())
if n - 1 < k:
    k = n-1
mod = 10**9+7
cmb1 = [1]*(n+1)
cmb2 = [1]*n
x = [0]*(n+1)
def Pow(a, n):
    if n == 0: return 1
    if n%2 == 0:
        return (Pow(a, n//2))**2%mod
    else:
        return Pow(a, n-1)*a%mod
for i in range(1,n+1):
    x[i] = Pow(i, mod-2)
for i in range(1,n+1):
    cmb1[i] = cmb1[i-1]*(n+1-i)%mod*x[i]%mod
for i in range(1,n):
    cmb2[i] = cmb2[i-1]*(n-i)%mod*x[i]%mod
ans = 0    
for i in range(k+1):
    ans = ((cmb1[i]*cmb2[i])%mod + ans)%mod
print(ans)