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, raw_input().split())
 
mod=10**9+7
fact, inv_fact = [1], [1]
fact_tmp = 1
for i in range(1,N+1):
    fact_tmp *= i
    fact_tmp %= mod
    fact.append(fact_tmp)
    inv_fact.append(pow(fact_tmp, mod-2, mod))
 
def ncr(n,r):
	if n < 0 or r < 0 or n < r:	return 0
	else:	return (fact[n] * inv_fact[r] * inv_fact[n-r]) %mod

can_zero_num=min(N-1,K)
ans=0
for zero_num in range(can_zero_num+1):
    ans+=ncr(N,zero_num)*ncr(N-1,N-zero_num-1)

print ans%mod