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
def pow(x, n, mod=None):
    ret = 1
    while n > 0:
        if n % 2 == 1:
            ret = (ret * x) % mod
        x = (x * x) % mod
        n >>= 1
    return ret
n,k = map(int,input().split())
mod = 10**9+7
fact = [None]*(1+n)
finv = [None]*(1+n)
fact[0] = 1
for i in range(1,n+1):
    fact[i] = (fact[i-1]*i)%mod
finv[n] = pow(fact[n],mod-2, mod=mod)
for i in range(n,0,-1):
    finv[i-1] = (finv[i]*i)%mod
def comb(n,k):
    tmp = (finv[n-k]*finv[k])%mod
    return (tmp*fact[n])%mod
ans = 0
for m in range(min(n,k+1)):
    ans = (ans+comb(n,m)*comb(n-1,m))%mod
print(ans)