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

f = [1]*(n+1)
for i in range(n):
  f[i+1] = f[i]*(i+1)%MOD
  
inv = [1]*(n+1)
inv[n] = pow(f[n], MOD-2, MOD)
for i in range(n,0,-1):
  inv[i-1] = inv[i] * i % MOD
  
def nCr(n, r):
  return f[n]*inv[n-r]*inv[r]%MOD

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

      
    
    