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: Wrong Answer)

####### 二項係数 C(n,k) mod pの計算 #######

MOD=10**9+7

## a**b mod p by 繰り返し二乗法 ##
def pow(a,b)
  return 1 if b==0
  return a*pow(a,b-1)%MOD if b%2==1
  return pow(a**2%MOD,b/2)
end

## n! mod p ##
def fact(n)
  ret=1
  n.times do |i|
    ret=ret*(i+1)%MOD
  end
  ret
end

## a**(-1) mod p ##
def inv(a)
  pow(a,MOD-2)%MOD
end

## C(n,k) mod p ##
def com(n,k)
  (fact(n)*inv(fact(k)))%MOD*inv(fact(n-k))%MOD
end

####################################

N,K=gets.split.map(&:to_i)
K=N-1 if N<=K

ans=0

for num in 2..K do
  ans+=com(N,num)*com(N-1,N-num-1)
  ans%=MOD
end

ans+=com(N,2)+1
ans%=MOD

puts ans