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
#  --*-coding:utf-8-*--

MOD = 10**9 + 7

def getModInv(a, b):
    return 1 if (a == 1) else (1-b*getModInv(b%a, a))//a%b


N, K = map(int, input().split())
t1, t2 = 1,1
s1, s2 = 1,1

for m in range(1, min(K, N-1)+1):
    t1 = t1*(N-m)*(N-m+1)%MOD
    t2 = t2*m**2%MOD

    s1 = (s1*t2 + s2*t1)%MOD
    s2 = s2*t2%MOD

print(s1*getModInv(s2, MOD)%MOD)

