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

R = 200010
f = [1]*R
p = 1
for i in range(1, R):
    p = f[i] = p*i%mod

finv = [1]*R
p = finv[-1] = pow(f[-1], mod-2, mod)
for i in range(R-2, 0, -1):
    p = finv[i] = p*(i+1)%mod

def comb(n, k):
    return f[n]*finv[n-k]*finv[k]%mod

ans = 0
for m in range(min(k, n-1)+1):
    x = comb(n, m)
    y = comb(n-1, m)
    ans += x*y%mod

print(ans%mod)