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 = list(map(int, input().split()))

mod = 10**9 + 7
k = min(k, n-1)

def choose(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = (x * (n-i+1)) % mod
        y = (y * i) % mod
    return (x * pow(y, mod-2, mod)) % mod

kaijo = [1]
for i in range(1,n+1): 
  kaijo.append(kaijo[i-1]*i % mod)

ans = 0
for i in range(k+1):
#    ans += (choose(n, min(i,n-i)) * choose(n-1, min(i,n-1-i))) % mod
    ans += kaijo[n] * pow(kaijo[i]*kaijo[n-i], mod-2,mod) * kaijo[n-1]*pow(kaijo[i]*kaijo[n-1-i],mod-2,mod)
    ans = ans % mod
print(ans % mod)
