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: Runtime Error)

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

ans = 0
lim = 2*(10**5) + 5
mothers = [1] * lim
mothers_inv = [1] * lim
for i in range(1, lim):
    mothers[i] = mothers[i-1] * i % mod
    mothers_inv[i] = pow(mothers[i], mod-2, mod)


def calc(n,k):
    child = mothers[n] * mothers_inv[n-k] % mod
    mother_inv = mothers_inv[k]
    return((child * mother_inv)%mod)

if( n <= k+1):
    ans = calc(2*n-1, n-1)
    print(ans)
    exit()

ans = calc(2*n-1, n-1)

tmp = 0
for i in range(1,n-k):
    if(i ==1):
        c1 = 1
    else:
        c1 = calc(n-1, i-1) 

    c2 = calc(n, i) 
    ans = (ans - c1 * c2)%mod


print(ans)