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
g1 = [1, 1]
g2 = [1, 1]
inv = [0, 1]
for i in range(2, n+1):
    g1.append((g1[-1] * i) % mod)
    inv.append((-inv[mod%i] * (mod//i)) % mod)
    g2.append((g2[-1] * inv[-1]) % mod)

def comb(n, r):
    if r<0 or r>n:
        return 0
    return g1[n] * g2[r] * g2[n-r] % mod

li = []
for i in range(min(k, n-1)+1):
    li.append(comb(n-1, i))
ans = 0
pre = 0
for cur in li:
    ans += (pre+cur)*cur
    pre = cur
print(ans%mod)