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
mod = 10**9+7
n,k = map(int,input().split())
ans = 0
mod = 10**9 + 7
inv_t = [0,1]
for i in range(2,n+2):
  inv_t += [inv_t[mod % i] * (mod - int(mod / i)) % mod]
a = n
b = n-1
for i in range(1,min(n,k)+1):
    ans += a*b % mod
    a = a*(n-i)*inv_t[i+1] % mod
    b = b*(n-i-1)*inv_t[i+1] % mod
    ans %= mod
if k > 1:
    ans += 1
print(ans % mod)
