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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(s)=parse(Int,s)
n,k=parseInt.(split(readline()))
MOD=10^9+7

fac=Array{Int}(2n)
ifac=Array{Int}(2n)
fac[1]=ifac[1]=1

function makefact(n,M=MOD)
    for i in 2:n
        fac[i]=(fac[i-1]*i)%M
        ifac[i]=invmod(fac[i],M)
    end
end

function CMOD(n,k,M=MOD)
    (k==0 || n==k ) && return 1
    return ((fac[n]*ifac[k])%M*ifac[n-k])%M
end
makefact(2n)

s=0
k=min(n-k,k)
for i in 0:k
    s += (CMOD(n,i)*CMOD(n-1,i))%MOD 
    s %= MOD
end
print(s)