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 PyPy3 (2.4.0) (judge verdict: Accepted)

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

fact = [1]*(n+1)
ans = 0
for i in range(1,n+1):
    fact[i] = fact[i-1]*i
    fact[i] %= mod
invfact = [1] * (n+1)
invfact[-1] = pow(fact[-1],mod-2,mod)
for i in range(n-1,0,-1):
    invfact[i] = (invfact[i+1]*(i+1))%mod
def C(x,y):
    if x<=y:return 1
    return fact[x]*invfact[y]*invfact[x-y]%mod


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