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 Rust (1.15.1) (judge verdict: Accepted)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

const R: u64 = 1000000007;

fn pow(n: u64, r: u64) -> u64 {
    let mut ret = 1;
    if r > 0 {
        ret = pow(n, r / 2);
        ret = ret * ret % R;
        if r % 2 == 1 {
            ret = ret * n % R;
        }
    }
    ret
}

fn main() {
    let nk: Vec<u64> = read_vec();
    let n = nk[0];
    let k = nk[1];

    let mut ans = 0;

    if k <= n - 2 {
        let mut a = n;
        let mut b = 1;
        for l in 2..n + 1 {
            a = (a * (n - l + 1)) % R;
            a = (a * pow(l, R - 2)) % R;
            b = (b * (n - l + 1)) % R;
            b = (b * pow(l - 1, R - 2)) % R;
            if l >= n - k {
                ans = (ans + ((a * b) % R)) % R;
            }
        }
    } else {
        ans = 1;
        for i in n + 1..2 * n {
            ans = (ans * i) % R;
        }
        for i in 1..n {
            ans = (ans * pow(i, R - 2)) % R;
        }
    }

    println!("{}", ans);
}