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

FAC = [1]
INV = [1]
for i in range(1,2*n+1):
  FAC.append((FAC[i-1]*i) % MOD)
  INV.append(pow(FAC[-1],MOD-2,MOD))

def nCr(n,r):
  return FAC[n]*INV[n-r]*INV[r]

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