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
import sys
n, k = map(int, input().split())

mod = 10 ** 9 + 7
f = [1]
for i in range(1,2*n+1):
    f.append((f[-1] * i) % mod)
def comb(n,r):
    return f[n] * (pow(f[r], mod-2, mod) * pow(f[n-r], mod-2, mod) % mod) % mod

ans = comb(2*n-1, n)
if n-1 <= k:
    print(ans)
    sys.exit()

j = 0
for i in range(k+1,n)[::-1]:
    ans -= (comb(n,n-i) * comb(n-1,j)) % mod
    ans %= mod
    j += 1

print(ans)