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 Python (3.8.2) (judge verdict: Accepted)

n, k = map(int, input().split())
mod = 1000000007

b = mod-2
blis = []
c = 0
while b >0:
  if b & 1 == 1:
    blis.append(c)
  c += 1
  b >>= 1

def modinv(a):
  if a == 1:
    return 1
  else:
    res = 1
    li = []
    for _ in range(c):
      li.append(a%mod)
      a = a*a%mod
    for item in blis:
      res = res *li[item] %mod
    return res

if k >=n:
  L = 2*n-1
  ansbunsi =1
  for j in range(n-1):
    ansbunsi = ansbunsi*L%mod
    L -= 1
  ansbunbo = 1
  L = n - 1
  for j in range(n-1):
    ansbunbo = ansbunbo*L%mod
    L -= 1
  ansbunbo = modinv(ansbunbo)
  print(ansbunsi*ansbunbo%mod)

else:
  kaijou = [1, 1]
  for j in range(2, n+1):
    kaijou.append(kaijou[-1]*j%mod)
  
  ans = 0

  for m in range(k+1):
    ansbunsi = kaijou[n]*kaijou[n-1]%mod
    ansbunbo = kaijou[m]*kaijou[n-m]%mod
    ansbunbo = ansbunbo*kaijou[n-m-1]%mod
    ansbunbo = ansbunbo*kaijou[m]%mod
    ansbunbo = modinv(ansbunbo)
    ans += ansbunbo*ansbunsi
    ans %= mod
  
  print(ans)