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
from collections import *
from itertools import *
from bisect import *
import copy

n,k=map(int,input().split())
mod=10**9+7
fac=[0,1]
for i in range(2,2*n+1):
    fac.append(fac[i-1]*i%mod)
ifac=[pow(i,mod-2,mod) for i in fac]

def comb(a,b):
    if a>=0 and b==0:return(1)
    if a<b or a<0:return(0)

    return((fac[a]*ifac[a-b]*ifac[b])%mod)

count=1
for m in range(1,min(k+1,n)):

    count=(count+comb(n,m)*comb(n-1,n-m-1))%mod
print(count)
