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 Python (3.4.3) (judge verdict: Wrong Answer)

M = 10 ** 9 + 7

def inv(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0

def comb(n, k):
    r1 = 1
    for i in range(k):
        r1 = r1 * (n - i) % M
    r2 = 1
    for i in range(k):
        r2 = r2 * (i + 1) % M
    return r1 * inv(r2, M) % M

def h(n, k):
    return comb(n + k - 1, k)

def solve(n, k):
    if k >= n:
        return h(n, n)
    r = 0
    for i in range(k + 1):
        r += comb(n, i) * h(n - i, i) % M
        # print('i=', i, 'r=', r)
        # print('h(n, i)=', h(n, i), 'h(n - i, i)=', h(n - i, i))
    return r

n, k = [int(x) for x in input().split()]
print(solve(n, k))