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
def comb_list(n, r, mod):
    ret = [1]
    for i in range(1, r+1):
        ret.append(ret[-1] * (n+1-i) * pow(i, mod-2, mod) % mod)
    return ret

n,k = map(int,input().split())
mod = 10**9+7

r = min(k,n-1)
ans = 0
nCl = comb_list(n, r, mod)
n1Cl = comb_list(n-1, r, mod)

for i in range(r+1):
    ans = (ans + nCl[i] * n1Cl[i]) % mod

print(ans)
