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
fac = [1]*(N+1)
rev = [1]*(N+1)
 
for i in range(1, N+1):
  fac[i] = i*fac[i-1]%MOD
  rev[i] = pow(fac[i], MOD-2, MOD)

comb = lambda a,b:(fac[a]*rev[a-b]*rev[b])%MOD
ans = 0

for i in range(1+min(N-1, K)):
  ans += comb(N, i) * comb(N-1, i)
ans %= MOD
print(ans)
