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 memfact(a,m):
    temp = 1
    yield temp
    for i in range(1,a+1):
        temp = temp * i % m
        yield temp
def comb(n,r,m):
    if r == 0: return 1
    return memf[n]*pow(memf[r],m-2,m)*pow(memf[n-r],m-2,m)

n,k = map(int, open(0).read().split())
dp = [0] * n
dp[0] = 1
m = 1000000007
dp[1] = (n * (n-1)) % m
memf = []
mfappend = memf.append
for x in memfact(n,m):
    mfappend(x)
for i in range(2,min(k+1,n)):
    dp[i] = (dp[i-1]+comb(n,i,m)*comb(n-1,i,m)) % m
print((dp[min(n-1,k)]+1)%m)