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
MAX = 4*10**5
bikkuri=[1]
mod = 10**9+7
for i in range(1,MAX+1):
    bikkuri.append((bikkuri[-1]*i)%mod)

def Comb(n,k):
    ans = bikkuri[n]*pow(bikkuri[k],mod-2,mod)*pow(bikkuri[n-k],mod-2,mod)
    ans %=mod
    return ans
    
n,k = map(int,input().split())
if n-1 <= k:
    ans = Comb(2*n-1,n)
    print(ans)
else:
    tmp = 0
    for i in range(k+1):
        tmp += Comb(n,i)*Comb(n-1,i)
        tmp %= mod
    print(tmp)