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 (7.3.0) (judge verdict: Time Limit Exceeded)

import bisect, collections, copy, heapq, itertools, math, string
import sys
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int, sys.stdin.readline().rstrip().split())
def LI(): return list(map(int, sys.stdin.readline().rstrip().split()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())

from  collections import defaultdict
import bisect
from functools import reduce
def main():
    def comb(n, r):
        numerator = reduce(lambda x, y: x * y % mod, [n - r + k + 1 for k in range(r)])
        denominator = reduce(lambda x, y: x * y % mod, [k + 1 for k in range(r)])
        return numerator * pow(denominator, mod - 2, mod) % mod
    mod = 10 ** 9 + 7
    N, K = MI()
    if K >= N - 1:
        ans = comb(2 * N - 1, N - 1)
        print(ans)
    else:
        N_r = pow(N, mod - 2, mod)
        ans = N * (N - 1) % mod
        if K >= 2:
            ans += 1
        for i in range(2, K + 1):
            ans += ((comb(N, i) ** 2 % mod) * ((N - i) % mod) * N_r) % mod
            ans %= mod
        print(ans)

if __name__ == "__main__":
    main()