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())
zero_end = min(n,k+1)

inv_mod = [pow(i,MOD-2,MOD) for i in range(zero_end)]

comb_mod1 = [1] * zero_end
comb_mod2 = [1] * zero_end
for i in range(1,zero_end):
    comb_mod1[i] = comb_mod1[i-1] * (n-i+1) * inv_mod[i] %MOD
    comb_mod2[i] = comb_mod2[i-1] * (n-i  ) * inv_mod[i] %MOD

ans = 0

for i in range(zero_end): 
    
    ans = ans + comb_mod1[i] *comb_mod2[i] %MOD
    
print(ans%MOD)