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
import sys
sys.setrecursionlimit(10**9)

MOD=10**9+7
n,k=map(int,input().split())

if k>=n-1:
  k=n-1

inv_table = [0]+[1]
for i in range(2,k+1):
  inv_table+=[inv_table[MOD%i]*(MOD-int(MOD/i))%MOD]

comb_sum=1
fact=1
comb1=1
comb2=1
for i in range(1,k+1):
  comb1=(comb1*(n-i+1)*inv_table[i])%MOD
  comb2=(comb2*(n-i)*inv_table[i])%MOD
  comb=(comb1*comb2)%MOD
  comb_sum+=comb

print(comb_sum%MOD)