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 = int(1e+9+7)

max_zero_num = min(n-1, k)
kai = [1]*(n+1)
gyaku_kai = [1]*(n+1)

for i in range(n):
    kai[i+1] = kai[i]*(i+1) % MOD
    gyaku_kai[i+1] = pow(kai[i+1], MOD-2, MOD)%MOD
        
answer = 0
for zero_num in range(max_zero_num+1):
    answer = (answer + kai[n]*gyaku_kai[n-zero_num]*gyaku_kai[zero_num]*\
    kai[n-1]*gyaku_kai[n-1-zero_num]*gyaku_kai[zero_num]) %MOD

print(answer)
