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
max_n=2*10**5
fac=[1]*(max_n+1)
inv=[1]*(max_n+1)
ifac=[1]*(max_n+1)
for n in range(2,max_n+1):
    fac[n]=(fac[n-1]*n)%MOD
    inv[n]=MOD-inv[MOD%n]*(MOD//n)%MOD
    ifac[n]=(ifac[n-1]*inv[n])%MOD
def comb(n,k):
    if n<k:
        return 0
    if n<0 or k<0:
        return 0
    return (fac[n]*ifac[k]*ifac[n-k])%MOD
print(sum([(comb(N,k)*comb(N-1,k))%MOD for k in range(min(N,K)+1)])%MOD)