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 = 10**9+7
def modinv(a, mod=10**9+7):
    return pow(a, mod-2, mod)

fac = [0]*(n+1)
fac[0] = 1
fac[1] = 1
for i in range(2,n+1):
    fac[i] = fac[i-1] * i % mod

def combi(n,r,mod=10**9+7):
    return( ( fac[n] * modinv(fac[r]) )%mod * modinv(fac[n-r]) % mod)

ans = 0
for i in range(min(k+1,n)):
    ans += combi(n,i)*combi(n-1,n-i-1) % mod
    ans %= mod
print(ans % mod)