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

fact = [0] * (n+1)
inv = [0] * (n+1)

fact[0], fact[1] = 1, 1
inv[0], inv[1] = 1, 1

for i in range(2,n+1):
	fact[i] = (fact[i-1] * i) % mod
for i in range(2,n+1):
	inv[i] = (inv[i-1] * pow(i, mod-2, mod)) % mod

if k >= n:
	k = n-1

def C(a,b):
	out = fact[a]
	out *= inv[b]
	out %= mod
	out *= inv[a-b]
	out %= mod
	return out

ans = 0
for m in range(k+1):
	ans += (C(n,m) * C(n-1,n-m-1)) % mod
	ans %= mod

print(ans)
	