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
 
fact = [1,1]
finv = [1,1]
inv = [0,1]
 
for i in range(2,2*n+1):
    fact.append((fact[-1]*i)%mod)
    inv.append((inv[mod%i]*(mod-mod//i))%mod)
    finv.append((finv[-1]*inv[-1])%mod)
 
def nCr(n,r,mod):
      
    return fact[n]*finv[r]*finv[n-r]%mod

def nHr(n,r,mod):
    return nCr(n+r-1,r,mod)



ans = 0

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