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] = list(map(int,input().split()))

mod = pow(10,9)+7

kaijo = [1]
for i in range(1,N+1): 
  kaijo.append(kaijo[i-1]*i % mod)

s =0
for m in range((K+1)*(N>K)+(N)*(K>=N)):
  s += (kaijo[N]*pow((kaijo[m]*kaijo[N-m]),mod-2,mod ))%mod * (kaijo[N-1]*pow((kaijo[m]*kaijo[N-1-m]),mod-2,mod ) )%mod
  s = s%mod

print(s)