Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

Solution in Ruby (2.3.3) (judge verdict: Accepted)

m=1000000007
n,k=gets.split.map &:to_i

def pmod(b, i, m)
  if i==0 then
    1
  elsif (i%2)==1 then
    b * pmod(b, i-1, m) % m
  else
    h = pmod(b, i/2, m)
    h*h%m
  end
end
    
def inv(a, p)
  pmod(a, p-2, p)
end

$f=Array.new(n+1)
$fi=Array.new(n+1)
$f[0]=1
n.times do|i|
  $f[i+1] = $f[i] * (i+1) % m
end
$fi[n] =inv($f[n],m)
n.times do|i|
  j=n-i
  $fi[j-1] = $fi[j] * j % m
end
def comb(n,k,m)
  $f[n]*$fi[k]%m*$fi[n-k]%m
end
t = 0
mn=[n,k+1].min

mn.times do|i|
  sel=comb(n,i,m)
  rem=n-i
  t+=sel*comb(n-1,i,m)%m
  t %= m
end
puts t