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)

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

numer = [ 1 ] * ( n + 1 )
demon = [ 1 ] * ( n + 1 )

for i in range( 1, n + 1 ):
  numer[ i + 1 ] = ( numer[ i ] * i ) % mod

demon[ n ] = pow( numer[ n ], mod - 2, mod )
for i in range( n, 0, -1 ):
  demon[ i - 1 ] = ( demon[ i ] * i ) % mod
  
def nCr( n, r ):
  if r < 1:
    return 0
  return ( numer[ n ] * demon[ r ] % mod ) * demon[ n - r ] % mod

ans = 0
for i in range( min( k, n - 1 ) + 1 ):
  ans = ( ans + nCr( n, i ) * nCr( n -1, i ) % mod
print( ans )