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

f = [ 1 ] * ( n + 1 ) 
inv = [ 1 ] * ( n + 1 )

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


