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 (3.4.3) (judge verdict: Runtime Error)

mod = 7+10**9

def expo(x,n):
  ans = 1
  while n>0:
    if n%2 == 1:
      ans = ans*x%mod
    x = x*x%mod
    n = n >> 1
  return ans

def fac(n):
  if not memo_f[n]:
    memo_f[n] = (n*fac(n-1))%mod
  return memo_f[n]

def combi(n,k):
  return (((fac(n)*(expo(fac(k),mod-2)))%mod)*expo(fac(n-k),mod-2))%mod


n,k = map(int,input().split())
memo_f = [1]+[0]*n

if k == 1:
  ans = combi(n-1,k)*combi(n,k)%mod
elif k >= n:
  ans = 0
  for i in range(n):
    ans = (ans + combi(n,i)*combi(n-1,i)%mod)%mod
else:
  ans = 0
  for i in range(k+1):
    ans = (ans + combi(n,i)*combi(n-1,i)%mod)%mod
print(ans)